Answer:
Option A - [tex]y=-\frac{5}{8}x+6[/tex]
Step-by-step explanation:
Given : Two points [tex](-8, 11)[/tex] and [tex](4,\frac{7}{2})[/tex]
To find : The equation represent the line
Solution :
The general form of the equation is [tex](y-y_1)=m(x-x_1)[/tex]
Where, m is the slope of the equation
First we find the slope of the equation [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex](x_1,y_1)=(-8,11)[/tex] and [tex](x_2,y_2)=(4,\frac{7}{2})[/tex]
Substitute the value,
[tex]m=\frac{\frac{7}{2}-11}{4-(-8)}[/tex]
[tex]m=\frac{\frac{-15}{2}}{12}[/tex]
[tex]m=-\frac{5}{8}[/tex]
Slope of the equation is [tex]m=-\frac{5}{8}[/tex]
Now, Take any point let [tex](x_1,y_1)=(-8,11)[/tex]
The equation form is [tex](y-11)=-\frac{5}{8}(x-(-8))[/tex]
[tex]y-11=-\frac{5}{8}(x+8)[/tex]
[tex]y-11=-\frac{5}{8}x-5[/tex]
[tex]y=-\frac{5}{8}x+6[/tex]
Therefore, Option A is correct.
The required equation is [tex]y=-\frac{5}{8}x+6[/tex]
