Question

Write an equation in slope intercept form for a line passing through the pair of points. Graph the line. (4, -2) and (8, -9)

Answer 1

The slope-intercept form of a line is:

y = mx + b

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

The slope is computed as follows:

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

where (x1,y1) and (x2, y2) are two known points. Replacing with (4, -2) and (8, -9):

$m=\frac{-9-(-2)}{8-4}=-\frac{7}{4}$

Replacing with the point (4, -2) and m = -7/4 into the general equation, we get:

-2 = (-7/4)4 + b

-2 = -7 + b

-2 + 7 = b

5 = b

Then, the equation is:

y = -7/4x + 5

The graph is