Question

Find the equation of a line that passes through left parenthesis 1 comma 6 right parenthesis(1,6) and is parallel to the graph of y equals 4 x plus 5y=4x+5. Write the equation in​ slope-intercept form, if possible.

Answer 1

The equation for the new line in slope-intercept form is:

`y=4x+2`

Explanation:

Since they give us an equation in slope-intercept form "y=4x+5", it is easy to extract the slope the new parallel line to this should have : "4" (same slope as the reference line)

We are also given a point the new line should go through : "(1, 6)"

So we can use the "point-slope" form of a line to find the equation of this new line:

`y-y_0=m(x=x_0)\\y=m(x-x_0)+y_0`

which for our case is:

`y=m(x-x_0)+y_0\\y=4\,(x-1)+6\\y=4x-4+6\\y=4x+2`