Answer:
see the explanation
Step-by-step explanation:
we have
[tex]y-3=-\frac{2}{3}(x+4)[/tex]
This is the equation of a line in point slope form
The slope is negative and equal to [tex]m=-\frac{2}{3}[/tex]
The line passes through the point (-4,3)
The y-intercept (value of y when the value of x is equal to zero) is
For x=0
[tex]y-3=-\frac{2}{3}(0+4)[/tex]
[tex]y-3=-\frac{8}{3}[/tex]
[tex]y=-\frac{8}{3}+3[/tex]
[tex]y=\frac{1}{3}[/tex]
The y-intercept is [tex](0,\frac{1}{3})[/tex]
The x-intercept (value of x when the value of y is equal to zero) is
For y=0
[tex]0-3=-\frac{2}{3}(x+4)[/tex]
[tex]\frac{9}{2}=(x+4)[/tex]
[tex]x=\frac{9}{2}-4[/tex]
[tex]x=\frac{1}{2}[/tex]
The x-intercept is [tex](0.5,0)[/tex]
see the attached figure to better understand the problem
