Question

Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Select three options

Answer 1

Two perpendicular lines will have slopes which are negative reciprocal to one another. This means, that, if one line has slope m, the other line will have slope n = -1/m. Likewise, m = -1/n; the reciprocal relationship goes both ways.
So, given the equation of the line in the question, we can find the slope by converting the equation to slope-intercept form.
5x - 2y = -6, becomes -2y = -5x - 6, becomes y = 5/2 + 3
So, if the original slope is 5/2, the slope of the perpendicular line will be the negative reciprocal, -2/5.
We also are given a point which the perpendicular line passes through, (5, -4).
Using the slope along with this point, we can find the y-intercept of the perpendicular line. Specifically, if y is -4 when x is 5, y will be (-4 - (5*(-2/5))) when x is 0. This gives us a y-intercept of (-4+2) or -2.
Putting this information together, we know the perpendicular line has a slope of -2/5 and a y-intercept of -2. Can you identify which equation(s) among your answer choices fit this information?

Answer 2

thx!