Question

Please help me determine the equation of the line in slope intercept form and show all work. A line that is perpendicular to the line

y = (1/2)x + 10 that passes through the
point (50,60).

Answer 1

y=-2x+160

Step by Step:

The equation of a line can be determined using the point slope formula:

y-y1=m (x-x1)

To make a substitution, we must ensure we have the correct information. The question gives:

y1=60

x1=50

y=1/2x+10 This is the formula of a line that is perpendicular to the one we are trying to find.

It tells us that the gradient of the perpendicular line is 1/2. The gradient of the line we are trying to find can be found using m1×m2=-1 because we know that when lines are perpendicular, the product of their gradients must equal 1

So if we replace m1 with 1/2

1/2×m2=-1

m2=-2

We now have all the relevant information to make a substitution:

y-60=-2 (x-50)

expand brackets

y-60=-2x+100

rearrange to get in the form y=mx+b

y=-2x+160