Question

Please help!

Passes through (-6, -1) and parallel to. x - y = 4
what is the equation of the line?

Answer 1

y = x + 5

Explanation:

1) First, find the slope of the line
`x-y = 4`. We can do this by setting it up in slope-intercept form, represented by the equation
`y = mx + b`. Whatever
`m` or the coefficient of the x-term is will be the slope. Isolate y in the equation:

`x-y = 4\\-y = -x+4\\y = x -4`

So, the slope of the given equation is 1. Parallel lines share the same slope, thus the slope of the new line will be 1 as well.

2) Now, use the point-slope formula
`y-y_1 = m (x-x_1)` to write the equation of the line in point-slope form. Substitute values for
`m`,
`x_1`, and
`y_1` in the formula.

Since
`m` is the slope, substitute 1 for it. Since
`x_1` and
`y_1` represent the x and y values of one point the line passes through, substitute the x and y values of (-6, -1) into those places as well. Then, isolate y in the resulting equation to put the equation in slope-intercept form and find the answer:

`y-(-1) = 1 (x-(-6))\\y + 1 = 1 (x + 6)\\y + 1 = x + 6\\y = x + 5`