Answer:
[tex]y+4=-\frac{1}{2} (x-5)[/tex]
This is the equation of the line perpendicular to the equation line through the points given that crosses through (-4,5)
Step-by-step explanation:
We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have a point given and a slope from the equation. We will chose point-slope since we have a point and can find the slope.
Point slope:[tex]y-y_1=m(x-x_1)[/tex]
We must find the slope using the graph. We pick two points which intersect with grid lines from the line given.
Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute [tex]x_1=3\\y_1=2[/tex] and [tex]x_2=2\\y_2=0[/tex]
[tex]m=\frac{0-2}{2-3}[/tex]
[tex]m=\frac{-2}{-1}=\frac{2}{1} =2[/tex]
[tex]m\neq 2[/tex] in our new equation because it is perpendicular to it. This means we will need to change it into its negative reciprocal which is [tex]m=-\frac{1}{2}[/tex].
We will substitute [tex]m=-\frac{1}{2}[/tex] and now use the point they gave us (-4,5) [tex]x_1=-4\\y_1=5[/tex].
[tex]y-(-4)=-\frac{1}{2} (x-5)[/tex]
[tex]y+4=-\frac{1}{2} (x-5)[/tex]
This is the equation of the line perpendicular to the equation line through the points given that crosses through (-4,5)
