Question

Can someone help me with this please? :)

Write an equation of a line perpendicular to line AB below in slope-intercept form that passes through the point (7, 6).

Answer 1

First step is to get all the information we need out of our starting line. We have it all but it's gradient.

The gradient of a line is = to the difference in the y co-ordinates of two points on the line divided by the difference in the two corresponding x co-ordinates on the line
\[y1-y2/x1-x2\]
\[5-1/-2-0 = 4/-2 = -2\]
Now we have the gradient it's smooth sailing.

The gradient of a line perpendicular can be worked out fairly easily because the graidents of any two perpendicular lines will multiply to = -1. So we just have to ask what can we multiply -2 by to get -1. 1/2 being the answer.

\[y-y1=m(x-x1) \] is the equation of any straight line when you know the gradient and 1 point it passes through. So all you need to do from here is sub in your gradient for m and sub in the ordinates for y1 and x1 and rearrange!

Answer 2

Thank you soo much! :)