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2. Graphs of Equations

Lines

2. Graphs of Equations

Lines

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The Slope of a Line

The Slope of a Line

Slope-Intercept Form

Slope-Intercept Form

Graphing Lines in Slope-Intercept Form

Graphing Lines in Slope-Intercept Form

Point-Slope Form

Point-Slope Form

Finding Equations of Lines Given Two Points

Finding Equations of Lines Given Two Points

Standard Form of Line Equations

Standard Form of Line Equations

Parallel & Perpendicular Lines

Parallel & Perpendicular Lines

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Find the Slope of a Line Passing Through Two Given Points

Find the Slope of a Line Passing Through Two Given Points

Finding the Slope of a Line

Finding the Slope of a Line

Relationship Between Slopes of Non-Vertical Parallel Lines

Relationship Between Slopes of Non-Vertical Parallel Lines

Relationship Between Slopes of Non-Vertical Perpendicular Lines

Relationship Between Slopes of Non-Vertical Perpendicular Lines

IB Sample Exam Question, Paper 1 Q5

IB Sample Exam Question, Paper 1 Q5

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Practice this topic

Multiple Choice

Find the slope of the line shown below.

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Multiple Choice

Find the slope of the line containing the points $\left(-1,1\right)$ and  $\left(4,3\right)$ .

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Multiple Choice

Write an equation of a line that passes through the point $\left(3,-4\right)$ and is parallel to the line  $x+2y+18=0$ .

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Multiple Choice

Graph a line with a slope of 0 that passes through the point $\left(3,-2\right)$ .

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Multiple Choice

Which of the following graphs below represents the equation $x=3$ ?

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Multiple Choice

In the graph shown, identify the y–intercept & slope. Write the equation of this line in Slope-Intercept form.

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Multiple Choice

Identify the 𝒚– intercept & slope of  $y=-2x-3$ . Then graph the equation.

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Multiple Choice

Write the point-slope form of the equation of a line with a slope of $-\frac25$ that passes through (1, 3). Then graph the equation.

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Multiple Choice

Write the point-slope form of the equation of a line with a slope of $0$ that passes through $\left(2,-4\right)$ . Then graph the equation.

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Multiple Choice

Write the point-slope form of the equation of a line that passes through the points $\left(2,1\right)$ and  $\left(-4,3\right)$ . Then graph the equation.

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Multiple Choice

Find the slope & $y-intercept$ of the line given by the equation $3x+2y-6=0$

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Multiple Choice

Graph the equation $9x+6y+18=0$ by finding the intercepts.

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Textbook Question

In Exercises 1–4, write an equation for line L in point-slope form and slope-intercept form.

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Textbook Question

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)

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Textbook Question

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

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Textbook Question

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (1,3), m = -2

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Textbook Question

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-5,4), m = -3/2

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Textbook Question

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)

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Textbook Question

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

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Textbook Question

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-8,4), undefined slope

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Textbook Question

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-1,3), and (3,4)

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Textbook Question

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.

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Textbook Question

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. x-intercept (3,0), y-intercept (0,-2)

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Textbook Question

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

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Textbook Question

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. horizontal, through (-7,4)

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Textbook Question

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. m=5, b=15

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Textbook Question

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)

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Textbook Question

Match each equation with the sketch that most closely resembles its graph. y = 5

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Textbook Question

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. slope 0, y-intercept (0, 3/2)

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Textbook Question

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

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Textbook Question

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

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Textbook Question

Find the slope and y-intercept of each line, and graph it. x+2y = -4

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Textbook Question

In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line. 2x + 3y + 6 = 0

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Textbook Question

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

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Textbook Question

The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines f.

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Textbook Question

Graph using intercepts: 2x - 5y - 10 = 0

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Textbook Question

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

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Textbook Question

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (-1, 4), parallel to x+3y=5

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Textbook Question

For each line, (a) find the slope and (b) sketch the graph. See Examples 6 and 7. 5x - 2y = 10

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Textbook Question

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (4, -4), perpendicular to x=4

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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.

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Textbook Question

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

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Textbook Question

Find and interpret the average rate of change illustrated in each graph.

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Textbook Question

Use a graphing calculator to solve each linear equation. 3(2x+1) - 2 (x-2) =5

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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)

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