Write an equation of the line that passes through (7,10) and is perpendicular to the line y=12x−9.

Answer 1

Perpendicular lines have reciprocal slopes and opposite signs for example: if a slope of a line is positive 9 the perpendicular line is -1/9.

start with the line y=12x-9 which is in the slope intercept form y=Mx+b where m is the slope

m= 12

perpendicular slope= -1/12

They gave us a point and we found our slope so we can use the point slope formula y-y₁=m(x-x₁) to find the line. Once you’ve plugged in the coordinate and the perpendicular slope you solve for y.

Answer 2

Hi Quaronna!

It is important to note that for an equation of a line to be perpendicular to another line, then the slopes of these equations must be the reciprocal of one another:

Since we want a line perpendicular to the line y = 12x - 9, our new equation must contain the slope (m) is -1/12

y = mx + b

10 = (-1/12)(7) + b

10 = (-7/12) + b

b = 127/12

y = (-1/12)x + 127/12