Question

Write an equation in slope-intercept form for the line passing through the following pair of points: (2, -6), -4, 3).

Answer 1

The equation in slope intercept form is $y=-\frac{3}{2} x-3$

Explanation:

The given pair of points are $(2,-6)$ and $(-4,3)$

The slope can be determined using the formula,

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting the points $(2,-6)$ and $(-4,3)$ in the slope formula, we have,

$m=\frac{3+6}{-4-2}$

$m=\frac{9}{-6}$

$m=-\frac{3}{2}$

The equation in slope intercept form can be determined using the formula,

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

Substituting $m=-\frac{3}{2}$ and the point $(2,-6)$ in the above formula, we get,

$y+6=-\frac{3}{2} (x-2)$

$y+6=-\frac{3}{2} x+3$

   $y=-\frac{3}{2} x+3-6$

   $y=-\frac{3}{2} x-3$

Thus, the equation in slope intercept form is $y=-\frac{3}{2} x-3$