Question

Whats the slope intercept form for the points [5,2] and [0,-1]

Answer 1

Answer:

$\displaystyle y=\frac{3}{5}x-1$

Step-by-step explanation:

The Equation of a Line

The equation of the line in slope-intercept form is:

$y=mx+b$

Where m is the slope and b the y-intercept.

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

$\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

We are given the points (5,2) and (0,-1), thus:

$\displaystyle y-2=\frac{-1-2}{0-5}(x-5)$

Operating:

$\displaystyle y-2=\frac{-3}{-5}(x-5)$

$\displaystyle y-2=\frac{3}{5}(x-5)$

To find the slope-intercept form, we continue to simplify the expression:

Removing the parentheses:

$\displaystyle y-2=\frac{3}{5}x-\frac{3}{5}\cdot 5$

$\displaystyle y-2=\frac{3}{5}x-3$

Adding 2:

$\displaystyle y=\frac{3}{5}x-3+2$

$\mathbf{\displaystyle y=\frac{3}{5}x-1}$