find equation of line

Question

Find the equation of the line in slope-intercept form that is perpendicular to the line 5x – 2y = 7 that passes through the point (-5, 3).

Answer 1

Sure thing.

So to find the equation of a line, we need a point and the slope. In this case, the point is given to us. All we need to do now is find the slope. What do we know about perpendicular lines?

The slope of a perpendicular line is always the negative reciprocal of the other line.

We are given 5x-2y = 7, we can shift this equation to get

-2y = 7-5x

y = -7/2 + 5/2x

So, our slope is 5/2x for the first line.

Since the perpendicular line is the negative reciprocal of this line, its slope is -2/5x.

So, now we can use point slope form to come to our final answer.

y-y₁ = m(x-x₁)

y - 3 = -2/5(x+5)