Question

Find the equation (in terms of xx ) of the line through the points (-2,4) and (3,-5)

Answer 1

Given the points (-2, 4) and (3, -5)

We will find the slope-intercept form of the equation of the line that passes through the given points.

The slope-intercept form is: y = m * x + b

where: m is the slope and (b) is the y-intercept

We will find the slope using the following formula:

$\begin{gathered} slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}$

So, the slope will be:

$m=\frac{-5-4}{3-(-2)}=\frac{-9}{5}$

substitute with (m):

$y=-\frac{9}{5}x+b$

substitute with the point (3, -5) to find the value of b:

$\begin{gathered} -5=-\frac{9}{5}\cdot3+b \\ -5=-\frac{27}{5}+b \\ b=-5+\frac{27}{5}=\frac{2}{5} \end{gathered}$

Substitute with (m) and (b) into the slope-intercept form:

So, the answer will be:

$y=-\frac{9}{5}x+\frac{2}{5}$