Question

Find the equation of the line that passes through (-1,2) and is perpendicular to 2y=2x−1. Leave your answer in the form y=mx+c

Answer 1

y=-x+1

Explanation:

since the line is perpendicular to 2y=2x-1, this means that its slope with be the opposite reciprocal of the line 2y=2x-1 's slope.

first, we should find the slope of the line 2y=2x-1:

2y=2x-1

y=x-1/2

therefore, the slope of 2y=2x-1 is 1.

the opposite reciprocal of 1 is -1.

so far, we have this:

y=-x+b

to find b (the y-intercept) we can plug the point (-1,2) into the equation we have so far and solve for b.

y=-x+b

2=-(-1)+b

2=1+b

b=1

so, the equation of the line that passes through (-1,2) and is perpendicular to 2y=2x-1 is:

y=-x+b

Answer 2

y = x + 3

Explanation:

given line in slope/intercept form:

y = x -1/2

slope of the perpendicular line = 1

equation of the line

y - 2 = x + 1

y = x + 3