Answer:
x-intercept is 2
y-intercept is [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
We can select any two points and find equation of line
(6,-3)
so, [tex]x_1=6,y_1=-3[/tex]
(10,-6)
so,[tex]x_2=10,y_2=-6[/tex]
Firstly, we will find slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
now, we can plug values
[tex]m=\frac{-6+3}{10-6}[/tex]
[tex]m=-\frac{3}{4}[/tex]
now, we can point slope form of line
[tex]y-y_1=m(x-x_1)[/tex]
we can plug values
[tex]y+3=-\frac{3}{4}(x-6)[/tex]
now, we can solve for y
[tex]y=-\frac{3}{4}x+\frac{3}{2}[/tex]
x-intercept:
we can set y=0
and then we can solve for x
[tex]0=-\frac{3}{4}x+\frac{3}{2}[/tex]
[tex]-\frac{3}{4}x=-\frac{3}{2}[/tex]
[tex]3x=6[/tex]
[tex]x=2[/tex]
y-intercept:
we can plug x=0
[tex]y=-\frac{3}{4}\times 0+\frac{3}{2}[/tex]
[tex]y=0+\frac{3}{2}[/tex]
we get
[tex]y=\frac{3}{2}[/tex]
So,
x-intercept is 2
y-intercept is [tex]\frac{3}{2}[/tex]
