Question

(1,3) and (0,-2) written in slope intercept form

Answer 1

We are given the following points:

$\begin{gathered} \mleft(1,3\mright) \\ \mleft(0,-2\mright) \end{gathered}$

To determine the slope-intercept form of the equation we need to use the following general form of a line equation:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept. The value of the slope is given by the following formula:

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

Where:

$\begin{gathered} (x_1,y_1)=(1,3) \\ (x_2,y_2)=(0,-2) \end{gathered}$

Replacing in the formula for the slope:

$m=\frac{-2-3}{0-1}$

Solving the operations:

$m=-\frac{5}{-1}=5$

Replacing the value of the slope:

$y=5x+b$

Now we replace the point (x,y) = (0,-2) to get the value of "b":

$\begin{gathered} -2=5(0)+b \\ -2=b \end{gathered}$

Replacing in the equation of the line:

$y=5x-2$