Answer:
[tex]y = -\frac{21}{2}x+5[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-4,47)[/tex]
[tex](x_2,y_2) = (2,-16)[/tex]
Required
The equation in slope intercept
First, calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where:
[tex](x_1,y_1) = (-4,47)[/tex]
[tex](x_2,y_2) = (2,-16)[/tex]
So:
[tex]m = \frac{-16 - 47}{2 - -4}[/tex]
[tex]m = \frac{-63}{6}[/tex]
Simplify
[tex]m = -\frac{21}{2}[/tex]
So, the equation is calculated as:
[tex]y = m(x - x_1) + y_2[/tex]
This gives:
[tex]y = -\frac{21}{2}(x - -4) + 47[/tex]
[tex]y = -\frac{21}{2}(x+4) + 47[/tex]
Open bracket
[tex]y = -\frac{21}{2}x-42 + 47[/tex]
[tex]y = -\frac{21}{2}x+5[/tex]
