Question

What is the equation of a line that passes through the points (-3, 4) and (2,8)?

Answer 1

Given that the line passes through the two points (-3,4) and (2,8)

We need to determine the equation of the line.

Slope:

The slope of the line can be determined using the formula,

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

Substituting the points (-3,4) and (2,8) in the above formula, we get;

$m=\frac{8-4}{2+3}$

$m=\frac{4}{5}$

Thus, the slope of the line is $m=\frac{4}{5}$

Equation of the line:

The equation of the line can be determined using the formula,

$y-y_1=m(x-x_1)$

Substituting the point (-3,4) and $m=\frac{4}{5}$ in the above formula, we have;

$y-4=\frac{4}{5}(x+3)$

$y-4=\frac{4}{5}x+\frac{12}{5}$

     $y=\frac{4}{5}x+\frac{12}{5}+4$

     $y=\frac{4}{5}x+\frac{32}{5}$

Thus, the equation of the line is $y=\frac{4}{5}x+\frac{32}{5}$