Answer:
[tex]y = \dfrac{4}{3}x -3[/tex]
Step-by-step explanation:
The slope-intercept form of a line is:
[tex]y=mx+b[/tex]
where:
- [tex]m[/tex] = slope
- [tex]b[/tex] = y-intercept
We can algebraically manipulate the given equation to be in this form by solving for y:
[tex]4x-3y=9[/tex]
↓ adding 3y to both sides
[tex]4x=9+3y[/tex]
↓ subtracting 9 from both sides
[tex]4x-9=3y[/tex]
↓ dividing both sides by 3
[tex]\boxed{y = \dfrac{4}{3}x -3}[/tex]
Further Note
From slope-intercept form, we can identify the following characteristics of this line:
- slope = 4/3
- y-intercept = -3
