Answer:
Option 1:[tex]y = -\frac{2}{3}x+5[/tex] is the correct answer.
Step-by-step explanation:
The slope-intercept form of a line is given as:
[tex]y = mx+b[/tex]
Here m is the slope and b is the y-intercept
m is calculated using the formula
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Given points are:
[tex](x_1,y_1) = (-3,7)\\(x_2,y_2) = (9,-1)[/tex]
Putting the values in the formula
[tex]m = \frac{-1-7}{9+3}\\= \frac{-8}{12}\\=\frac{-2}{3}[/tex]
Putting m=-2/3 in equation
[tex]y= -\frac{2}{3}x+b[/tex]
Putting (9,-1) in equation
[tex]-1 = -\frac{2}{3}(9)+b\\-1 = -6+b\\b = -1+6\\b = 5[/tex]
Putting the value of b
[tex]y = -\frac{2}{3}x+5[/tex]
Hence,
Option 1:[tex]y = -\frac{2}{3}x+5[/tex] is the correct answer.
