Question

Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.(2, -3). (4, 5)

Answer 1

The equation in slope-intercept form is:

$y=mx+b$

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

To find it for the given points, we can use this equation to find the slope first:

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

Since we have the points (2, -3) and (4, 5):

$\begin{gathered} x_1=2_{}_{}_{} \\ y_1=-3 \\ x_2=4 \\ y_2=5 \\ m=\frac{5-(-3)}{4-2}=\frac{5+3}{2}=\frac{8}{2}=4 \end{gathered}$

To get to the slope-intercept, we can first use the slope and one of the point to write it in the slope-point form:

$\begin{gathered} y-y_1_{}=m(x-x_1) \\ y+3=4(x-2) \end{gathered}$

And solve for y to get to the answer:

$\begin{gathered} y+3=4x-8 \\ y=4x-11 \end{gathered}$