Question

How do you write an equation in slope-intercept form for the line that passes through `(4,-2)` and is parallel to the graph of `y=1/2x-7`?

Answer 1

`y=1/2 x -4`

Explanation:

Equation of line through `(4,-2)` and parallel to `y=1/2 x-7`

The given equation is in the form `y=mx+b`, where `m=`slope.

Parallel lines have equal slopes, so the slope of the line we are trying to find is `m=1/2`.

Next, use the point-slope form of a line:

`y-y_1=m(x-x_1)` where `(x_1,y_1)` is a point on the line.

`y- -2=1/2 (x-4)`

`y+2=1/2 x -2`
`color(white)a-2color(white)(aaaaaa)-2`

`y=1/2 x -4`

OR

Use the slope intercept form of a line (again with `m= 1/2`):

`y=mx+b` where `b=`the `y` intercept.

Plug in `(4,-2)` for `x and y` and solve for `b`.

`-2=1/2 (4)+b`

`-2=color(white)(aa^2)2+b`
`-2=-2`

`-4=b`

The equation is then `y= 1/2 x-4`