Question

1. what is the slope-intercept form of the equation $-2x + 3y = 9$?

a. $y = -\frac{2}{3}x + 3$
b. $y = \frac{2}{3}x + 9$
c. $y = \frac{2}{3}x + 3$
d. $y = -\frac{2}{3}x + 9$

Explanation:

Step1: Isolate the y-term

Add $2x$ to both sides.
$$-2x + 3y + 2x = 9 + 2x$$
$$3y = 2x + 9$$

Step2: Solve for y

Divide all terms by 3.
$$y = \frac{2x}{3} + \frac{9}{3}$$
$$y = \frac{2}{3}x + 3$$

Answer:

c. $y = \frac{2}{3}x + 3$