Transform 3y+3x=9

Question

to slope-intercept form y=mx+b
by solving for y
.

This question is worth two points--one for the correct answer and one for showing your solving steps. You can either type your work into the box below using the math characters button or upload a picture of your work if you wrote it on paper.

(2 points)

Answer 1

To transform the equation \( 3y + 3x = 9 \) into slope-intercept form \( y = mx + b \), follow these steps:

1. Start with the original equation: \[ 3y + 3x = 9 \]

2. Isolate the \( y \) term: Subtract \( 3x \) from both sides: \[ 3y = 9 - 3x \]

3. Divide every term by 3 to solve for \( y \): \[ y = \frac{9}{3} - \frac{3x}{3} \] This simplifies to: \[ y = 3 - x \]

4. Rewrite for slope-intercept form: To express it in the standard form \( y = mx + b \), we can rearrange: \[ y = -x + 3 \]

Now, the equation in slope-intercept form is: \[ y = -x + 3 \]

• Here, the slope \( m = -1 \) and the y-intercept \( b = 3 \).

Final answer: \[ y = -x + 3 \]

Steps shown:

1. \( 3y + 3x = 9 \)
2. \( 3y = 9 - 3x \)
3. \( y = 3 - x \)
4. \( y = -x + 3 \)

(2 points: 1 for the correct answer and 1 for showing steps of work.)