Question

Write the equation of the line in slope-intercept form that has the following points: (2, -1)(5, -3)

Answer 1

Answer:

$\large\boxed{y=-\dfrac{2}{3}x+\dfrac{1}{3}}$

Step-by-step explanation:

The skope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

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

We have the points (2, -1) and (5, -3). Substitute:

$m=\dfrac{-3-(-1)}{5-2}=\dfrac{-3+1}{3}=\dfrac{-2}{3}=-\dfrac{2}{3}$

We have the equation:

$y=-\dfrac{2}{3}x+b$

Put the coordinates of the point (2 , -1) to the equation:

$-1=-\dfrac{2}{3}(2)+b$

$-1=-\dfrac{4}{3}+b$           add 4/3 to both sides

$\dfrac{1}{3}=b\to b=\dfrac{1}{3}$

Finally we have:

$y=-\dfrac{2}{3}x+\dfrac{1}{3}$