Question

What is an equation of the line that passes through the point (8, 2) and is

parallel to the line 5x – 4y = 36?

Answer 1

`5x - 4y = 36 \\ 4y = 5x - 36 \\ y = (5)/(4) x - 9`

When the point is (8,2) and slope is 5/4

`y = mx + c \\ 2 = (5)/(4) * 8 + c \\ 2 = 10 + c \\ \boxed{c = - 8} \\`

Putting the value of c=-8, we get

`y = (5)/(4) x - 8 \\ 4y = 5x - 32 \\ \boxed{5x - 4y = 32} \: is \: the \: required \: equation.`

Answer 2

Explanation:

5x - 4y = 36

4y = 5x - 36

y = 1.25x - 9

Since this line has a slope of 1.25, the parallel line will also have a slope of 1.25.

=> y = 1.25x + c

When x = 8, y = 2.

=> (2) = 1.25(8) + c

=> 2 = 10 + c, c = -8

Hence the line equation is y = 1.25x - 8.