Question

How do I write an equation in slope intercept form for a line that satisfies points (4,5) and (-2,5)?

Answer 1

`y=5`

Explanation:

`"calculate the slope m using the "color(blue)"gradient formula"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))`

`"let "(x_1,y_1)=(4,5)" and "(x_2,y_2)=(-2,5)`

`rArrm=(5-5)/(-2-4)=0/(-6)=0`

`"this indicates that the line is horizontal and parallel to the"`
`"x-axis passing through all points in the plane with a "`
`"y-coordinate of 5, for this reason the equation is"`

`y=5`
graph{y-0.001x-5=0 [-20, 20, -10, 10]}

Answer 2

`y=0x+5`

Explanation:

First find the slope. Then determine the point-slope form of the line, and then solve for `y` to get the slope-intercept form of the line.

First use the slope formula to determine the slope from the two points.

`m=(y_2-y_1)/(x_2-x_1)`,

where:

`m` is the slope, and the points are `(x_1,y_1)` and `(x_2,y_2)`. Either point can be point 1 or 2. I'm going to use `(4,5)` as point 1, and `(-2,5)` as point 2.

Plug in the known values and solve for `m`.

`m=(5-5)/(-2-4)`

`m=0/(-6)`

`m=0`

Another way to look at slope is `m=("rise")/("run")`, where the rise is the change in `y` and the run is the change in `x`. In a horizontal line, the slope is `0` because there is no rise (no change in y). So all points would have the same `y`-value. Any line with a slope of zero is horizontal.

Now we need to determine the point-slope form of the line.

`y-y_1=m(x-x_1)` `larr` You can use either of the two points given above. I'm going to use `(4,5)` for `(x_1,y_1)`.

Plug in the known values.

`y-5=0(x-4)`

To get to slope-intercept form, solve the point-slope form for `y`.

`y-5=0(x-4)`

Expand the right-hand side.

`y-5=0x`

Add `5` to both sides.

`y=5`

The graph is horizontal at `y=5`, so all points will have `5` as their `y`-value. The `x`-value is infinite. You can easily find the points `(4,5)` and `(-2,5)` on the line on the graph below.

graph{y=0x+5 [-14.24, 14.23, -7.12, 7.12]}