Answer:
[tex]y-7=-\frac{\displaystyle 4}{\displaystyle 9}(x+4)[/tex]
OR
[tex]y-3=-\frac{\displaystyle 4}{\displaystyle 9}(x-5)[/tex]
Step-by-step explanation:
Hi there!
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point that falls on the line
1) Determine the slope (m)
[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-4, 7) and (5, 3):
[tex]m=\frac{\displaystyle 3-7}{\displaystyle 5-(-4)}\\\\m=\frac{\displaystyle 3-7}{\displaystyle 5+4}\\\\m=\frac{\displaystyle -4}{\displaystyle 9}[/tex]
Therefore, the slope of the line is [tex]-\frac{\displaystyle 4}{\displaystyle 9}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex] as [tex]m[/tex]:
[tex]y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)[/tex]
2) Plug a point into [tex]y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)[/tex]
[tex]y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)[/tex]
Because we're given two points, there are two ways we can write this equation:
[tex]y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)\\\\y-7=-\frac{\displaystyle 4}{\displaystyle 9}(x-(-4))\\\\y-7=-\frac{\displaystyle 4}{\displaystyle 9}(x+4)[/tex]
OR
[tex]y-3=-\frac{\displaystyle 4}{\displaystyle 9}(x-5)[/tex]
I hope this helps!
