Doug C. answered • 09/25/21
Math Tutor with Reputation to make difficult concepts understandable
To find the slope of the original line, isolate/solve for y to place the equation in slope-intercept form. The slope of the line is the numerical coefficient of x.
The slope of the line perpendicular to the original line will be the negative reciprocal of the slope of the original.
As an example, if the slope of the original line is 8/5, the slope of the perpendicular will be -5/8.
For the given problem, the point which the perpendicular passes through is given as (0,-4), which also happens to be the y-intercept, so b in the "formula" y=mx+b) is -4. That allows you to immediately write the equation of the perpendicular as y = mx - 4 where m is the calculated slope. For point-slope:
y - (-4) = m (x-0). To write the equation in standard form you probably will have to clear the equation of fractions before writing something like Ax + By + C = 0 where A,B,C are integers.
Once you have tried the above here is where you can check your work:
desmos.com/calculator/2uoeprscnh
