What is the equation of the line through (3,7) that is perpendicular to the line through points (-1,-2) and (5,3)?: ')

The equation of the line would by y = -6/5x + 53/5

Step-by-step explanation:

In order to find this, we must first find the slope of the original line. We can do this with the slope formula.

m (slope) = (y2 - y1)/(x2 - x1)

m = (3 - -2)/(5 - -1)

m = (3 + 2)/(5 + 1)

m = 5/6

Now that we have the slope of this line, we can find the slope to the other line by using the reciprocal and opposite of it. So we flip 5/6 to get 6/5 and then we make it negative to get -6/5. Now that we have this, we can use the slope and a point in point-slope form to find the line.

y - y1 = m(x - x1)

y - 7 = -6/5(x - 3)

y - 7 = -6/5x + 18/5

y = -6/5x + 53/5

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