Answer:
[tex]y =2x + 3[/tex]
Step-by-step explanation:
Given
(-2,-1) and (3,9).
Required
Determine the line equation
First, we calculate slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (-2,-1)[/tex]
[tex](x_2,y_2) = (3,9)[/tex]
So, we have:
[tex]m = \frac{9 - (-1)}{3- (-2)}[/tex]
[tex]m = \frac{9+1}{3+2}[/tex]
[tex]m = \frac{10}{5}[/tex]
[tex]m = 2[/tex]
The equation is then calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - (-1) =2(x - (-2))[/tex]
[tex]y - (-1) =2(x +2)[/tex]
[tex]y +1 =2(x +2)[/tex]
Open bracket
[tex]y +1 =2x + 4[/tex]
Subtract 1 from both sides
[tex]y +1-1 =2x + 4-1[/tex]
[tex]y =2x + 3[/tex]
