# Lines - Video Tutorials & Practice Problems

## The Slope of a Line

Find the slope of the line shown below**.**

$m=1$

$m=\frac23$

$m=\frac32$

$m=3$

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

$m=\frac52$

$m=\frac25$

$m=2$

$m=\frac43$

## Types of Slope

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

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

## Slope-Intercept Form

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

****

$y=\frac23x+1$

$y=-\frac23x+1$

$y=-2x+1$

$y=x+2$

## Graphing Lines in Slope-Intercept Form

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

$b=-2,m=-3$

$b=-3,m=-2$

$b=\frac23,m=-3$

$b=2,m=-3$

## Point-Slope Form

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**.**

$y-3=-\frac25\left(x-1\right)$

$y-3=x-1$

$y+3=\frac25\left(x+1\right)$

$y=-\frac25x-1$

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**.**

$y+4=x-2$

$y+4=x$

$y+4=0$

$y=0$

## Finding Equations of Lines Given Two Points

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**.**

$y-1=-\frac13\left(x-2\right)$

$y-3=-\frac13\left(x-2\right)$

$y=\frac13x-4$

$y-2=-\frac13\left(x-1\right)$

## Standard Form of Line Equations

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

$m=2,b=-3$

$m=-\frac32,b=3$

$m=3,b=-\frac32$

$m=\frac23,b=2$

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

## Parallel & Perpendicular Lines

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

$y+4=-\frac12\left(x-3\right)$

$y+4=-2\left(x-3\right)$

$y=-\frac12\left(x-3\right)$

$y-3=-\frac12\left(x+4\right)$

## Do you want more practice?

- In Exercises 1–4, write an equation for line L in point-slope form and slope-intercept form.
- In Exercises 1–10, find the slope of the line passing through each pair of points or state that the slope is u...
- In Exercises 9–12, use the given conditions to write an equation for each line in point-slope form and general...
- Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-inte...
- Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-inte...
- In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-...
- 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...
- Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-inte...
- In Exercises 19–24, write an equation in slope-intercept form of a linear function f whose graph satisfies the...
- In Exercises 17–24, a) List all possible rational roots. b) List all possible rational roots. c) Use the quoti...
- In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-...
- Match each equation with the sketch that most closely resembles its graph. y = 5
- In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-...
- In Exercises 41–44, use the given conditions to write an equation for each line in point-slope form and slope-...
- Find the slope and y-intercept of each line, and graph it. x+2y = -4
- In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line. ...
- In Exercises 49–58, graph each equation in a rectangular coordinate system. y = -2
- The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an ...
- Graph using intercepts: 2x - 5y - 10 = 0
- Find the slope of each line, provided that it has a slope. through (0, -7) and (3, -7)
- Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (-1, 4...
- For each line, (a) find the slope and (b) sketch the graph. See Examples 6 and 7. 5x - 2y = 10
- Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (4, -4...
- In Exercises 59-66, a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. ...
- For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. throu...
- For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. throu...
- For each line described, write an equation in(a)slope-intercept form, if possible, and(b)standard form. throu...
- Find and interpret the average rate of change illustrated in each graph.
- Use a graphing calculator to solve each linear equation. 3(2x+1) - 2 (x-2) =5
- 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 slop...
- Retaining the Concepts. If f(x) = 4x^2 - 5x - 2, find [f(x + h) - f(x)]/h, h ≠ 0
- Exercises 143–145 will help you prepare for the material covered in the next section. If (x1,y1) = (-3, 1) and...