A line is parallel to 5x+2y-8=0 and has the same y-intercept as x+4y-12=0

Question

Find an equation for the line.

Answer 1

first make each into y=mx+b by rearranging

5x+2y-8=0
2y=-5x+8
y=-5/2x +4

and

x+4y-12=0
4y=-x+12
y=-1/4x+3

because the line is parallel to the first equation it will have the same value for the slope (m)

y=-5/2x+b

now use the second equation to solve for the value of y at the y intercept (i.e. we know x is zero, solve y)

y=-1/4x+3
y=-1/4(0)+3
y=3

so the y intercept of our new equation is (x,y)=(0,3)

put this into our new equation to solve for b

y=-5/2x+b
3=-5/2(0)+b
3=b

so our new equation is

y=-5/2x+3