find an equation for a line with slope and a point

Question

Find the equation of a line parallel to 2x+5y=1, with the same y-int as x-4y=8

Answer 1

Given that equation of line is parallel to 2x + 5y = 1

And also given that required line has same intercepts as x - 4y = 8.

Given line is 2x + 5y = 1

5y = 1 - 2x

y = -(2/5)x + 1/5

It is in the form of y = mx + c

Slope of the given line is m1 = -(2/5)

Parallel slope is m1 = m2 = -(2/5)

Another given line is x - 4y = 8

-4y = -x + 8

y = (1/4) x  -2

y - intercept is -2  and slope is -(2/5) for the required line equation.

Therefore the required equation is y = -(2/5)x - 2