Answer:
y = (8/7)x + 33/7
Explanation:
First, we need to calculate the slope of the line. So, we can use the following equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are the coordinates of two points in the line.
We can replace (x1, y1) with (-5, -1) and (x2, y2) with (2, 7) and get that the slope is equal to:
[tex]m=\frac{7-(-1)}{2-(-5)}=\frac{7+1}{2+5}=\frac{8}{7}[/tex]Now, the equation of a line with slope m that passes through the point (x1, y1) is:
[tex]y-y_1=m(x-x_1)[/tex]So, replacing m by 8/7 and (x1, y1) by (-5, -1), we get that the equation is:
[tex]\begin{gathered} y-(-1)=\frac{8}{7}(x-(-5)) \\ y+1=\frac{8}{7}(x+5) \end{gathered}[/tex]Finally, we can solve the equation for y and get:
[tex]\begin{gathered} y+1=\frac{8}{7}x+\frac{8}{7}(5) \\ y+1=\frac{8}{7}x+\frac{40}{7} \\ y+1-1=\frac{8}{7}x+\frac{40}{7}-1 \\ y=\frac{8}{7}x+\frac{33}{7} \end{gathered}[/tex]Therefore, the answer is:
y = (8/7)x + 33/7