Question

rewriting equations in slope-intercept form homework
rewrite each of the following equations in slope-intercept form: y = mx + b.

1. 8x - 4y = 20
2. 2x + 3y = 12
3. 2x + y = -11
4. 0.8x + 0.4y = 1.2
5. 3y = 4x - 27
6. x - 4y = 8
7. y + 9 = 2(x + 5)
8. y - 1 = \\(\frac{2}{3}\\)(x + 3)

Explanation:

Problem 1: \( 8x - 4y = 20 \)

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

Subtract \( 8x \) from both sides:
\( -4y = -8x + 20 \)

Step 2: Solve for \( y \)

Divide every term by \( -4 \):
\( y = \frac{-8x}{-4} + \frac{20}{-4} \)
Simplify:
\( y = 2x - 5 \)

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

Subtract \( 2x \) from both sides:
\( 3y = -2x + 12 \)

Step 2: Solve for \( y \)

Divide every term by \( 3 \):
\( y = \frac{-2x}{3} + \frac{12}{3} \)
Simplify:
\( y = -\frac{2}{3}x + 4 \)

Step 1: Isolate \( y \)

Subtract \( 2x \) from both sides:
\( y = -2x - 11 \)

Answer:

\( y = 2x - 5 \)

Problem 2: \( 2x + 3y = 12 \)