Daniel C. answered • 23d

Undergraduate student at Vanderbilt University: ACT + SAT prep

The first step I would do toward solving this problem is to get the equation in __slope-intercept form____.__

4x + y = 5

y = -4x + 5

This is the equation of the line to which we want to find a perpendicular line. Remember that the slope of a line perpendicular to another line is the ** negative reciprocal** of its slope. In slope intercept form, with an isolated y, the slope is the coefficient of the x term. So the negative reciprocal of the slope is the negative reciprocal of -4, which would be 1/4

So now that we know that the slope of the perpendicular line is 1/4, we must find the y-intercept.

I usually think of this in two ways. Firstly, you can sketch a graph and plot a point at (8,8), and since you know the slope (rise/run) is 1/4, you can work backwards to find the y-intercept.

The algebraic way to do this is to put the point and slope into ** point-slope form**: y-y

_{1}= m(x-x

_{1})

where m is the slope and (x_{1},y_{1}) is your point. Plugging this in you get:

y - 8 = 1/4(x - 8)

Now you only have to solve for y in slope-intercept form

y - 8 = (1/4)x - 2

y = (1/4)x + 6

This is your final answer, the equation of a line perpendicular to 4x + y = 5 and passing through the point (8,8) in slope-intercept form is

**y = (1/4)x + 6**