Question

Write an equation of each line that passes through the following points in slope-intercept form:

Answer 1

Answer:

$\large\boxed{y=\dfrac{8}{5}x-3}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points M(5, 5) and N(-10, -19). Substitute:

$m=\dfrac{-19-5}{-10-5}=\dfrac{-24}{-15}=\dfrac{8}{5}$

We have the equation:

$y=\dfrac{8}{5}x+b$

Put the coordinates of the point M to the equation:

$5=\dfrac{8}{5}(5)+b$

$5=8+b$        subtract 8 from both sides

$-3=b\to b=-3$

Finally we have the equation:

$y=\dfrac{8}{5}x-3$