Question

How do you find the equation of a line passing through (4, 1) with the slope m = -1/2?

Answer 1

See below:

Explanation:

Point `(x_1, y_1)=(4, 1)`

Slope (`m`) `=-1/2`

Let the equation of the line be

`y-y_1=m(x-x_1)`

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

`y-1=-1/2x+2`

`x/2+y=3`

which is the required equation of the line.

Answer 2

`y=-1/2x+3`

Explanation:

Slope-intercept form of a line: `y=mx+b`, with `m` as the slope and `b` as the y-intercept

We know that the slope is `-1/2`, so we can put that in for `m`:

`y=-1/2x+b rarr` To find the y-intercept, plug in the point `(4, 1)` and solve

`1=-1/2*4+b`

`1=-2+b`

`b=3`

The equation in slope-intercept form is `y=-1/2x+3`