4.5 Use the Slope-Intercept Form of an Equation of a Line

Before you get started, take this readiness quiz.

Add: $\frac{x}{4} + \frac{1}{4} .$
If you missed this problem, review the reference.

Find the reciprocal of $\frac{3}{7} .$
If you missed this problem, review the reference.

Solve $2 x - 3 y = 12 \text{for} y$.
If you missed this problem, review the reference.

Identify the slope and y-intercept of the line $y = \frac{2}{5} x - 1$.

Identify the slope and y-intercept of the line $y = - \frac{4}{3} x + 1$.

Identify the slope and y-intercept of the line $x + 4 y = 8$.

Identify the slope and y-intercept of the line $3 x + 2 y = 12$.

Determine the most convenient method to graph each line.

ⓐ $y = −6$ ⓑ $5 x - 3 y = 15$ ⓒ $x = 7$ ⓓ $y = \frac{2}{5} x - 1$.

Determine the most convenient method to graph each line: ⓐ $3 x + 2 y = 12$ ⓑ $y = 4$ ⓒ $y = \frac{1}{5} x - 4$ ⓓ $x = −7$.

Determine the most convenient method to graph each line: ⓐ $x = 6$ ⓑ $y = - \frac{3}{4} x + 1$ ⓒ $y = −8$ ⓓ $4 x - 3 y = −1$.

Use slopes and y-intercepts to determine if the lines $3 x - 2 y = 6$ and $y = \frac{3}{2} x + 1$ are parallel.

Use slopes and y-intercepts to determine if the lines $2 x + 5 y = 5 \text{and} y = - \frac{2}{5} x - 4$ are parallel.

Use slopes and y-intercepts to determine if the lines $4 x - 3 y = 6 \text{and} y = \frac{4}{3} x - 1$ are parallel.

Use slopes and y-intercepts to determine if the lines $y = −4$ and $y = 3$ are parallel.

Use slopes and y-intercepts to determine if the lines $y = 8 \text{and} y = −6$ are parallel.

Use slopes and y-intercepts to determine if the lines $y = 1 \text{and} y = −5$ are parallel.

Use slopes and y-intercepts to determine if the lines $x = −2$ and $x = −5$ are parallel.

Use slopes and y-intercepts to determine if the lines $x = 1$ and $x = −5$ are parallel.

Use slopes and y-intercepts to determine if the lines $x = 8$ and $x = −6$ are parallel.

Use slopes and y-intercepts to determine if the lines $y = 2 x - 3$ and $−6 x + 3 y = −9$ are parallel. You may want to graph these lines, too, to see what they look like.

Use slopes and y-intercepts to determine if the lines $y = - \frac{1}{2} x - 1$ and $x + 2 y = 2$ are parallel.

Use slopes and y-intercepts to determine if the lines $y = \frac{3}{4} x - 3$ and $3 x - 4 y = 12$ are parallel.

Use slopes to determine if the lines, $y = −5 x - 4$ and $x - 5 y = 5$ are perpendicular.

Use slopes to determine if the lines $y = −3 x + 2$ and $x - 3 y = 4$ are perpendicular.

Use slopes to determine if the lines $y = 2 x - 5$ and $x + 2 y = −6$ are perpendicular.

Use slopes to determine if the lines, $7 x + 2 y = 3$ and $2 x + 7 y = 5$ are perpendicular.

Use slopes to determine if the lines $5 x + 4 y = 1$ and $4 x + 5 y = 3$ are perpendicular.

Use slopes to determine if the lines $2 x - 9 y = 3$ and $9 x - 2 y = 1$ are perpendicular.

Identify the slope and y-intercept of each line.

$y = −9 x + 7$

Identify the slope and y-intercept of each line.

$y = 4 x - 10$

Identify the slope and y-intercept of each line.

$4 x + y = 8$

Identify the slope and y-intercept of each line.

$8 x + 3 y = 12$

Identify the slope and y-intercept of each line.

$7 x - 3 y = 9$

Determine the most convenient method to graph each line.

$y = 4$

Determine the most convenient method to graph each line.

$x = −3$

Determine the most convenient method to graph each line.

$y = −5 x + 2$

Determine the most convenient method to graph each line.

$x - y = 1$

Determine the most convenient method to graph each line.

$y = \frac{4}{5} x - 3$

Determine the most convenient method to graph each line.

$y = −1$

Determine the most convenient method to graph each line.

$2 x - 5 y = −10$

Determine the most convenient method to graph each line.

$y = - \frac{1}{3} x + 5$

Use slopes and y-intercepts to determine if the lines are parallel.

$y = \frac{2}{3} x - 1 ; 2 x - 3 y = - 2$

Use slopes and y-intercepts to determine if the lines are parallel.

$3 x - 4 y = - 2 ; y = \frac{3}{4} x - 3$

Use slopes and y-intercepts to determine if the lines are parallel.

$6 x - 3 y = 9 ; 2 x - y = 3$

Use slopes and y-intercepts to determine if the lines are parallel.

$8 x + 6 y = 6 ; 12 x + 9 y = 12$

Use slopes and y-intercepts to determine if the lines are parallel.

$x = 7 ; x = - 8$

Use slopes and y-intercepts to determine if the lines are parallel.

$x = - 3 ; x = - 2$

Use slopes and y-intercepts to determine if the lines are parallel.

$y = 5 ; y = 1$

Use slopes and y-intercepts to determine if the lines are parallel.

$y = - 1 ; y = 2$

Use slopes and y-intercepts to determine if the lines are parallel.

$4 x + 4 y = 8 ; x + y = 2$

Use slopes and y-intercepts to determine if the lines are parallel.

$5 x - 2 y = 11 ; 5 x - y = 7$

Use slopes and y-intercepts to determine if the lines are parallel.

$4 x - 8 y = 16 ; x - 2 y = 4$

Use slopes and y-intercepts to determine if the lines are parallel.

$x - 5 y = 10 ; 5 x - y = - 10$

Use slopes and y-intercepts to determine if the lines are parallel.

$9 x - 5 y = 4 ; 5 x + 9 y = - 1$

Use slopes and y-intercepts to determine if the lines are perpendicular.

$x - 4 y = 8 ; 4 x + y = 2$

Use slopes and y-intercepts to determine if the lines are perpendicular.

$2 x + 3 y = 5 ; 3 x - 2 y = 7$

Use slopes and y-intercepts to determine if the lines are perpendicular.

$3 x - 4 y = 8 ; 4 x - 3 y = 6$

Use slopes and y-intercepts to determine if the lines are perpendicular.

$2 x + 4 y = 3 ; 6 x + 3 y = 2$

Use slopes and y-intercepts to determine if the lines are perpendicular.

$2 x - 6 y = 4 ; 12 x + 4 y = 9$

Use slopes and y-intercepts to determine if the lines are perpendicular.

$8 x - 2 y = 7 ; 3 x + 12 y = 9$

The equation $n = 4 T - 160$ is used to estimate the number of cricket chirps, n, in one minute based on the temperature in degrees Fahrenheit, T.

1. ⓐ Explain what the slope of the equation means.
2. ⓑ Explain what the n–intercept of the equation means. Is this a realistic situation?

Why are all horizontal lines parallel?