Question

If the slope of a line and a point on the line are known, the equation of the line can be found using the slope-intercept form, y=mx+b. To do so, substitute the value of the slope and the values of x and y using the coordinates of the given point, then determine the value of b. Using the above technique, find the equation of the line containing the points (-2,7) and (4,-2).

Answer 1

The general slope - intercept form of the line is ;

$y=mx+b$

where m is the slope, b is y-intercept

We need to find the equation of the line containing the points ( -2 , 7 ) and ( 4 , -2 )

The slope will be calculated as following:

$m=\frac{-2-7}{4-(-2)}=\frac{-9}{6}=-\frac{3}{2}$

So, the equation of the line will be :

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

using the point ( -2 , 7 ) to find b:

So, when x = -2 , y = 7

so,

$\begin{gathered} 7=-\frac{3}{2}\cdot-2+b \\ 7=3+b \\ b=7-3=4 \end{gathered}$

so, the equation of the line is:

$y=-\frac{3}{2}x+4$