Answer:
[tex]\large\boxed{y=\dfrac{8}{5}x-3}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points M(5, 5) and N(-10, -19). Substitute:
[tex]m=\dfrac{-19-5}{-10-5}=\dfrac{-24}{-15}=\dfrac{8}{5}[/tex]
We have the equation:
[tex]y=\dfrac{8}{5}x+b[/tex]
Put the coordinates of the point M to the equation:
[tex]5=\dfrac{8}{5}(5)+b[/tex]
[tex]5=8+b[/tex] subtract 8 from both sides
[tex]-3=b\to b=-3[/tex]
Finally we have the equation:
[tex]y=\dfrac{8}{5}x-3[/tex]
