Question

Which of the following equations represents the line that passes throught the points (2, -6) and (-4,3)?

Answer 1

First, find the slope of the line that goes through the 2 given points, which you should know how to do.  Call it m.  Then a perpendicular line must have a slope of -1/m.  The slope-intercept form of the equation you seek is

y = (-1/m)x + b,

where b is any real number.  Examine the list of choices, and pick any that have a slope of -1/m.

Answer 2

The equation that represents the line that passes through the points (2, -6) and (-4,3) is 2y + 3x = -6.

How to find the equations represent the line that passes through the points (2, -6) and (-4,3)?

The equation of the line that passes through the points (x1,y1) and (x2,y2) can be obtained with the formula:

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

The slope of the points are

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

We need to find the equation that represents the line that passes through the points (2, -6) and (-4,3)

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

$m=\dfrac{3+6}{-4-2}\\\\\\ m = 9/-6 = -3/2$

So, the equation is:

$y-y_1 = m (x-x_1)\\\\y +6 = -3/2(x -2)\\\\2y +12 = -3x +6\\\\2y + 3x = -6$

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