Question

convert each equation below to slope-intercept form, then graph. show all work!

1. $8x - 2y = -14$

$-8x$ $-8x$
$\frac{-2y}{-2}=\frac{-8x - 14}{-2}$
$y = 4x + 7$
$m=\frac{4}{1}$ rise over run $(0,7)$
graph for problem 13

1. $x + y = 2$

$-x$ $-x$
$y = -x + 2$
graph for problem 14

Explanation:

Problem 13: \( 8x - 2y = -14 \)

Step 1: Isolate the \( y \)-term

Subtract \( 8x \) from both sides:
\( -2y = -8x - 14 \)

Step 2: Solve for \( y \)

Divide every term by \( -2 \):
\( y = \frac{-8x}{-2} + \frac{-14}{-2} \)
Simplify:
\( y = 4x + 7 \)

Problem 14: \( x + y = 2 \)

Step 1: Isolate the \( y \)-term

Subtract \( x \) from both sides:
\( y = -x + 2 \)

Answer:

s:

1. Slope-intercept form: \( \boldsymbol{y = 4x + 7} \)
2. Slope-intercept form: \( \boldsymbol{y = -x + 2} \)

(For graphing:

• For \( y = 4x + 7 \): Plot the \( y \)-intercept \( (0, 7) \), then use slope \( 4 \) (rise \( 4 \), run \( 1 \)) to draw the line.
• For \( y = -x + 2 \): Plot the \( y \)-intercept \( (0, 2) \), then use slope \( -1 \) (rise \( -1 \), run \( 1 \)) to draw the line.)