Answer:
The equation is [tex]y=\frac{13}{4} x-24[/tex]
Solution:
Here, [tex]x_{1}=4 ; y_{1}=-8 ; x_{2}=8 ; y_{2}=5[/tex]
We know the slope of an equation is given by y=m x+c
To find the value of m, we use the below given formula
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Substituting the values we get,
[tex]\mathrm{m}=\frac{5-(-8)}{8-4}[/tex]
[tex]\mathrm{m}=\frac{5+8}{4}[/tex]
[tex]\therefore m=\frac{13}{4}[/tex]
Substituting the value of m in the slope intercept form we get,
[tex]y=\frac{13}{4} x+c[/tex]
To find the The value of c, we substitute the value of x and y from any two given point. Let us take x = 4 and y = -8
[tex]\Rightarrow-8=\frac{13}{4}(4)+\mathrm{c}[/tex]
[tex]\Rightarrow-8=13+c[/tex]
[tex]\Rightarrow-8-13=c[/tex]
[tex]\Rightarrow-21=c[/tex]
Therefore, the slope intercept equation becomes [tex]y=\frac{13}{4} x-21[/tex]
