through (8,5) perpendicular to 2x-y=7

Question

I need help with this. I have to give the equation in slope-intercept form and standard form. I know perpendicular lines are a negative reciprocal.

Answer 1

2x - y = 7 is in standard form, and if it were slope-intercept form that would help you. I got the y term by itself:

y = 2x - 7 slope-intercept form. You already know the slope of the perpendicular line is the *negative reciprocal* of the slope you have. So that's (-1/2). The perpendicular line is something like

y = -(1/2)x + b and if you substitute 8 for x and 5 for y you get 9 for b.

y = -(1/2)x + 9 is your perpendicular line. In slope-intercept form. To get back to standard form, start by getting rid of fractions. Multiply both sides by 2.

2y = -x + 18 then add x to both sides.

 

x + 2y = 18 done.

Sanity check: sketch the lines, see if they LOOK perpendicular. I did this with Wolfram Alpha.