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
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
