Question

What is an equation of the line that passes through the point left bracket, 8, comma, minus, 5, right bracket(8,−5) and is parallel to the line x, plus, 4, y, equals, 8x+4y=8?​

Answer 1

y = -2x +11

Explanation:

As we are searching for the equation to a straight line, our template equation will be:

y = mx + c

First we must solve for m, the gradient of our function, which can be found by rearranging the parallel line equation into the general from:

8x + 4y = 8

∴ 4y = -8x +8

∴ y = -2x + 2

Returning to our y = mx +c formula, we can see that the parallel line has a gradient of -2. Parallel line will always have the same gradient, and so this is also the gradient of our function, which we can now write like this:

y = -2x +c

To find c, we now substitute in the given point (8, -5) in place of x and y.

-5 = -2(8) +c

-5 = -16 +c

c = 11

∵ y = -2x +11

Hope that help!