Question

Graph the equation 9−x=3/2y
9
−
𝑥
=
3
/
2
𝑦
using slope-intercept form.

Answer 1

Start by solving for y (slope-intercept form y = mx + b):

9 − x = (3/2) y
y = (2/3)(9 − x) = (2/3)·9 − (2/3)x = 6 − (2/3)x

Rewrite as y = (−2/3)x + 6. So slope m = −2/3 and y-intercept b = 6.

To graph:
- Plot the y-intercept (0, 6).
- Use the slope −2/3: from (0,6) go right 3 and down 2 to get (3,4). Repeat to get (6,2) and (9,0).
- Draw a straight line through these points (extend in both directions).

You can also check the x-intercept by setting y = 0: 0 = −(2/3)x + 6 → x = 9, consistent with point (9,0).