Answer:
[tex]y = 4x-1[/tex]
Step-by-step explanation:
Required:
Determine the equation of the linear function
First, we need to determine the slope (m) as follows:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (-2,-9)[/tex]
[tex](x_2,y_2) = (4,15)[/tex]
Substitute these values in [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{15- (-9)}{4 - (-2)}[/tex]
[tex]m = \frac{24}{6}[/tex]
[tex]m =4[/tex]
The equation is then calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
This gives:
[tex]y -(-9) = 4(x - (-2))[/tex]
[tex]y + 9 = 4(x + 2)[/tex]
[tex]y + 9 = 4x + 8[/tex]
Make y the subject
[tex]y = 4x + 8 - 9[/tex]
[tex]y = 4x-1[/tex]
