Question

converting equations in slope-intercept form
rewrite the following equations in slope - intercept form. you must show each step.

1. $3y - 15 = -6x$
2. $-5x + 6y = 12$
3. $-2x = y - 2$

Explanation:

Problem 1: \( 3y - 15 = -6x \)

Step 1: Add 15 to both sides

To isolate the term with \( y \), we add 15 to both sides of the equation.
\( 3y - 15 + 15 = -6x + 15 \)
Simplifying, we get \( 3y = -6x + 15 \)

Step 2: Divide by 3

To solve for \( y \), we divide every term in the equation by 3.
\( \frac{3y}{3} = \frac{-6x}{3} + \frac{15}{3} \)
Simplifying each term, we have \( y = -2x + 5 \)

Step 1: Add \( 5x \) to both sides

To isolate the term with \( y \), we add \( 5x \) to both sides of the equation.
\( -5x + 5x + 6y = 5x + 12 \)
Simplifying, we get \( 6y = 5x + 12 \)

Step 2: Divide by 6

To solve for \( y \), we divide every term in the equation by 6.
\( \frac{6y}{6} = \frac{5x}{6} + \frac{12}{6} \)
Simplifying each term, we have \( y = \frac{5}{6}x + 2 \)

Step 1: Add 2 to both sides

To isolate \( y \), we add 2 to both sides of the equation.
\( -2x + 2 = y - 2 + 2 \)
Simplifying, we get \( y = -2x + 2 \)

Answer:

\( y = -2x + 5 \)

Problem 2: \( -5x + 6y = 12 \)