Question

What is the equation of the line that passes through the point of intersection of the lines y = 2x − 5 and y = −x + 1, and is also parallel to the line y = 1/2x + 4

Answer 1

Y=1/2x-2

To find the point where the two lines intersect they are set equal to each other so that x can be found:
2x-5=-x+1
2x+x=1+5
3x=6
x=2

If x is known, x can be plugged into one of the two equations to find y.
y=-x+1=-2+1=-1

This means the point where they intersect is (2,-1).
We also know that the slope has to be 1/2 because the slope has to match the slope of the line it is parallel to.

Putting this into point slope form, we get:
(y-(-1))=1/2(x-2)

Which can be simplified into slope intercept form:
y+1=1/2x-1
y=1/2x-1-1
y=1/2x-2