3. Functions and Graphs

Write and Graph the Slope-Intercept Form of the Equation of a Line

Linear Functions and Slope

Slope-Intercept Form of the Equation of a Line

In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = −1, passing through (−4, − 1/4)

Graphing Lines in Slope-Intercept Form (y = mx + b)

In Exercises 49–58, graph each equation in a rectangular coordinate system. y = -2

Find the slope of each line, provided that it has a slope. through (2, -2) and (3, -4)

Exercises 143–145 will help you prepare for the material covered in the next section. Solve for y: 3x + 2y − 4 = 0.

In Exercises 19–24, write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ passes through (−6, 4) and is perpendicular to the line that has an x intercept of 2 and a y-intercept of -4.

For the linear function f(x) = mx + b, f(−2) = 11 and ƒ(3) = -9. Find m and b.

In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = - 3/5, passing through (10, −4)

If one point on a line is (2, −6) and the line's slope is -3/2, find the y-intercept.

In Exercises 1–10, find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (4, 7) and (8, 10)

In Exercises 59-66,
a. Rewrite the given equation in slope-intercept form.
b. Give the slope and y-intercept.
c. Use the slope and y-intercept to graph the linear function. 
4y+ 28 = 0

Write an equation in point-slope form and slope-intercept form of the line passing through (-10,3) and (-2,-5).

In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (-2, 0) and (0, 2)

Find the slope of each line, provided that it has a slope. through (0, -7) and (3, -7)

In Exercises 67–72, use intercepts to graph each equation. 6x-9y-18 = 0

Create appropriate linear relationships by graphing

Retaining the Concepts. If f(x) = 4x^2 - 5x - 2, find 
[f(x + h) - f(x)]/h, h ≠ 0

Find the Slope of a Line Passing Through Two Given Points

Find the Linear Function Passing Through Two Given Points

In Exercises 67–72, use intercepts to graph each equation. 6x-3y+15=0

In Exercises 79–80, find the value of y if the line through the two given points is to have the indicated slope. (3, y) and (1, 4), m = −3

Finding the equation and slope of a vertical line

In Exercises 39–48, give the slope and y-intercept of each line whose equation is given. Then graph the linear function. f(x) = (3/4)x-2

In Exercises 13-18, find the average rate of change of the function from 1 to 2. f(x) = x² + 2x from x₁ = 3 to x2 = 5

In Exercises 41–44, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (-3, 2) with slope - 6

For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. 
x - intercept (-3, 0), y-intercept (0, 5)

n Exercises 5–8, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (2, −3) and perpendicular to the line whose equation is y = (1/5)x + 6

Secant Line: Finding an Equation for a Secant Line

Graphing Linear Functions by Finding X,Y Intercept

Graph lines in standard form

In Exercises 1–10, find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (-2, 1) and (2, 2)

In Exercises 19–24, write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ passes through (−1, 5) and is perpendicular to the line whose equation is x = 6.

Exercises 143–145 will help you prepare for the material covered in the next section. Find the ordered pairs ( ______, 0) and (0, _______) satisfying 4x-3y-6=0.

In Exercises 81–82, graph each linear function. 6x-5f(x) - 20 = 0

Ex 1:  Graph a Linear Equation in Standard Form Using the Intercepts

Find the slope of a linear function using two points

In Exercises 39–48, give the slope and y-intercept of each line whose equation is given. Then graph the linear function. y = -2x/5+6

In Exercises 49–58, graph each equation in a rectangular coordinate system. 3x -18=0

In Exercises 13-18, find the average rate of change of the function from 1 to 2. f(x) = 3x from x1 = 0 to x2 = 5

In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = 8, passing through (4, −1)

In Exercises 59-66,
a. Rewrite the given equation in slope-intercept form.
b. Give the slope and y-intercept.
c. Use the slope and y-intercept to graph the linear function. 
8x – 4y – 12 =0

Find the slope of each line, provided that it has a slope. through (5, 6) and (5, -2)

General form of a linear equation

Exercises 143–145 will help you prepare for the material covered in the next section. If (x1,y1) = (-3, 1) and (x2, y2) = (−2, 4), find (y2-y1)/(x2-x1)

In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (−3, 6) and (3, −2)

Finding the Slope of a Line

In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (−2, −4) and (1, −1)

Find the slope of each line, provided that it has a slope. through (8, 7) and (1/2, -2)

In Exercises 77-78, give the slope and y-intercept of each line whose equation is given. Assume
that B ≠ 0. Ax = By - C

In Exercises 17–24, a) List all possible rational roots. b) List all possible rational roots. c) Use the quotient from part (b) to find the remaining roots and solve the equation. 6x^3+25x^2−24x+5=0

Graph function not written in slope-intercept form

Linear Regression - Least Squares Criterion  Part 1

Graphing a Line Using a Point and Slope

For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. 
through (0, 5), perpendicular to 8x+5y=3

In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. x-intercept = -1/2 and y-intercept = 4

Increasing, Decreasing, Horizontal and Vertical Lines

Write an equation in point-slope form and slope-intercept form for the line passing through (-2, -6) and perpendicular to the line whose equation is x − 3y+ 9 = 0.

Finding a Mathematical Expression to Model a Situation - Basic Example

In Exercises 1–4, write an equation for line L in point-slope form and slope-intercept form. <p><img src="https://lightcat-files.s3.amazonaws.com/problem_images/aa7c1418c7e1362d-1676829564070.jpg" alt="" /></p>

Find the slope of each line, provided that it has a slope. 11x + 2y = 3

Definition of a Linear Equation In Two Variables

 Find the Slope of a Line Given in Standard Form

In Exercises 49–58, graph each equation in a rectangular coordinate system. f(x) = 1

For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. 
through (-2, 4) and (1, 3)

 Equations of Horizontal and Vertical Lines

 Point-Slope Form of the Equation of a Line

In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = -5, passing through (-4, -2)

Graphing a Linear Equation using Intercepts

Graph lines in slope intercept form

In Exercises 9–12, use the given conditions to write an equation for each line in point-slope form and general form. Passing through (5, −9) and perpendicular to the line whose equation is x + 7y - 12= 0

Create the appropriate linear relationship by using a table to find the intercepts

In Exercises 19–24, write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ passes through (−2, 6) and is perpendicular to the line whose equation is x = -4.

In Exercises 37–40, find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (-1, -2) and (-3, -4)

In Exercises 9–12, use the given conditions to write an equation for each line in point-slope form and general form. Passing through (4, −7) and perpendicular to the line whose equation is x − 2y – 3 = 0

In Exercises 1–10, find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (4, -1) and (3, −1)

Graphing a Simple System of Equations

y-y1 = m(x - x1) Find the Equation of a Line Using Point-Slope Form

How to Graph Linear Equations Special Lines Horizontal Vertical Lines

In Exercises 19–24, write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ is perpendicular to the line whose equation is 3x - 2y - 4 = 0 and has the same y-intercept as this line.

In Exercises 33–34, find and simplify the difference quotient [f(x + h) - f(x)]/h, h =/= 0 for the given function. f(x) = -2x^2 + x + 10

In Exercises 1–4, write an equation for line L in point-slope form and slope-intercept form. <p><img src="https://lightcat-files.s3.amazonaws.com/problem_images/b59cfccf0f81978a-1676828904964.jpg" alt="" /></p>

In Exercises 41–44, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (-3, 6) and perpendicular to the line whose equation is y = (1/3)x + 4

Graphing Lines in Standard Form (ax + by = c)

Linear Regression - Least Squares Criterion  Part 2

In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = 2, passing through (3, 5)

In Exercises 59-66,
a. Rewrite the given equation in slope-intercept form.
b. Give the slope and y-intercept.
c. Use the slope and y-intercept to graph the linear function. 4x+y-6=0

Graphing Lines in Algebra: Understanding Slopes and Y-Intercepts

In Exercises 13-18, find the average rate of change of the function from 1 to 2. f(x) = √x from x₁ = 4 to x2 = 9

For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. 
through (2, -10), perpendicular to a line with undefined slope.

n Exercises 5–8, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (−8, −10) and parallel to the line whose equation is y = −4x + 3

In Exercises 73–76, find the slope of the line passing through each pair of points or state that the slope is undefined. Assume that all variables represent positive real numbers. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (-a, 0) and (0, -b)

Solve real world problems using slope and y-intercept

In Exercises 17–24, a) List all possible rational roots. b) List all possible rational roots. c) Use the quotient from part (b) to find the remaining roots and solve the equation. x^4−2x^3−5x^2+8x+4=0

Graph lines in point slope form

In Exercises 9–12, use the given conditions to write an equation for each line in point-slope form and general form. Passing through (−2, 2) and parallel to the line whose equation is 2x-3y-7=0

For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. 
through (3, -5) with slope -2.

In Exercises 39–48, give the slope and y-intercept of each line whose equation is given. Then graph the linear function. f(x) = -2x+1

In Exercises 41–44, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (4, -7) and parallel to the line whose equation is 3x + y - 9 = 0.

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