Question

write the equation of a line with the same slope as y-3=-2(x+1) and a solution of (4,10) in slope intercept form

Answer 1

`y=-2x+18`

Explanation:

We start by noticing that the given line:
`y-3=-2\,(x+1)` is given in "point slope" form, where the slope (m) is "-2".

We need therefore another line with same slope (m = -2) and which goes through the point (4, 10), which will make it solution of the line equation.

We can use the general form of a line in "point slope" form with slope "m" , and going through the point
`(x_0,y_0)` on the plane as:

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

For our case: m = -2 and
`y-y_0=m\,(x-x_0)` = (4, 10) this becomes:

`y-y_0=m\,(x-x_0)\\y-10=-2\,(x-4)\\y-10=-2x+8\\y=-2x+8+10\\y=-2x+18`