Answer:
[tex]y=-\frac{8}{9}x+\frac{8}{3}[/tex]
Or
[tex]9y+8x-24=0[/tex]
Step-by-step explanation:
The line passes through [tex](-6,8)[/tex]
The x-intercept being 3 means the line also passes through [tex](3,0)[/tex].
We can use the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The slope of the given line is [tex]m=\frac{0-8}{3--6}[/tex]
This simplifies to
[tex]m=-\frac{8}{9}[/tex].
[tex]y-0=-\frac{8}{9}(x-3)[/tex]
This gives
[tex]y=-\frac{8}{9}x+\frac{8}{3}[/tex]
This is the slope-intercept form.
When we multiply through by 9, we get,
[tex]9y=-8x+24[/tex]
Or
[tex]9y+8x-24=0[/tex]
