Question

rewriting equations in slope-intercept form
the equation of a line written in the form $y = mx + b$ is said to be in slope-intercept form. to write an equation in slope-intercept form, you need to isolate $y$ by using the properties of equality.
example:
rewrite the equation $4x - 2y = 12$ in slope-intercept form.
$\

$$\begin{align*} 4x - 2y &= 12\\\\ -4x \\quad \\quad -4x\\\\ -2y &= -4x + 12\\\\ \\frac{-2y}{-2} &= \\frac{-4x}{-2} + \\frac{12}{-2}\\\\ y &= 2x - 6 \\end{align*}$$

$

1. subtract $4x$ from each side to isolate $y$.
2. simplify.
3. divide each term by $-2$ to get $y$ by itself.
4. simplify.

rewrite each of the following equations in $y = mx + b$ form. show each step!

1. $x + y = -15$
2. $2y + 8x = 1$
3. $-2x + y = 1$
4. $3y - 2x = 9$
5. $2y = -1x - 8$
6. $y - 4 = -3(x - 3)$

Explanation:

Problem 1: \( x + y = -15 \)

Step1: Subtract \( x \) from both sides

\( x + y - x = -15 - x \)

Step2: Simplify

\( y = -x - 15 \)

Step1: Subtract \( 8x \) from both sides

\( 2y + 8x - 8x = 1 - 8x \)

Step2: Simplify

\( 2y = -8x + 1 \)

Step3: Divide each term by 2

\( \frac{2y}{2} = \frac{-8x}{2} + \frac{1}{2} \)

Step4: Simplify

\( y = -4x + \frac{1}{2} \)

Step1: Add \( 2x \) to both sides

\( -2x + y + 2x = 1 + 2x \)

Step2: Simplify

\( y = 2x + 1 \)

Answer:

\( y = -x - 15 \)

Problem 2: \( 2y + 8x = 1 \)