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-y1 = m(x-x1)
where m is the slope and (x1,y1) 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
