Question

Write the equation of the line passing through the point (1, 1/2) and perpendicular to the line y+4x=6

Answer 1

Perpendicular lines have slopes that are negative reciprocals. That means that when you multiply the slopes together, you get -1.

First you need to find the slope of y + 4x = 6. Then you find the slope of the perpendicular.
To find the slope of y + 4x = 6, just solve that equation for y. Then you'll have the equation in the form y = mx + b, where m = the slope.
y + 4x = 6
y = -4x + 6
m = -4. Slope of this line is -4; slope of the perpendicular is 1/4 since (-4)(1/4) = -1

Now you need to find the equation of the line that passes through point (1, 1/2) and has slope 1/4.
Use the form y = mx + b, insert the point (1, 1/2) in for x and y, insert 1/4 for m and solve for b:
y = mx + b
1/2 = (1/4)(1) + b
2 = 1 + b
b = 1, so
y = (1/4)x + 1