Question

Find the equation (in terms of xx ) of the line through the points (-4,1) and (3,-2)

Answer 1

First, find the slope of the line that passes through the given points using the slope formula:

$m=\frac{\Delta y}{\Delta x}$

Next, substitute the value of the slope and the coordinates of one of the given points into the slope-intercept form of the equation of a line to find the y-intercept b:

$y=mx+b$

Compute the value of the slope:

$\begin{gathered} m=\frac{(-2)-(1)}{(3)-(-4)} \\ =\frac{-2-1}{3+4} \\ =\frac{-3}{7} \\ =-\frac{3}{7} \end{gathered}$

Replace m=-3/7, x=-4 and y=1 into the slope-intercept form of the equation of a line:

$\begin{gathered} \Rightarrow1=-\frac{3}{7}(-4)+b \\ \Rightarrow1=\frac{12}{7}+b \\ \Rightarrow1-\frac{12}{7}=b \\ \Rightarrow-\frac{5}{7}=b \\ \therefore b=-\frac{5}{7} \end{gathered}$

Replace m=-3/7 and b=-5/7 to get the equation of the line through the points (-4,1) and (3,-2):

$y=-\frac{3}{7}x-\frac{5}{7}$

Therefore, the answer is:

$y=-\frac{3}{7}x-\frac{5}{7}$