Question

What is the slope-intercept form of the line passing through `(5, 1)` and `(0, -6)`?

Answer 1

The general slope intercept form of a line is

`y=mx+c`

where `m` is the slope of the line and `c` is its `y`-intercept (the point at which the line cuts the `y` axis).

Explanation:

First, get all the terms of the equation. Let us calculate the slope.

`"slope" = (y_2-y_1)/(x_2-x_1)`

`=(-6-1)/(0-5)`

`= 7/5`

The `y`-intercept of the line is already given. It is `-6` since the `x` coordinate of the line is zero when it intersects the `y` axis.

`c=-6`

Use the equation.

`y=(7/5)x-6`

Answer 2

`y=1.4x+6`

Explanation:

`P-=(5,1)`
`Q-=(0,-6)`
`m=(-6-1)/(0-5)=-7/-5`
`m=1.4`
`c=1-1.4xx5=1-7`
`c=6`
`y=mx+c`
`y=1.4x+6`

Answer 3

One answer is: `(y-1)=7/5(x-5)`
the other is: `(y + 6)=7/5(x-0)`

Explanation:

The slope-intercept form of a line tells you what you need to find first: the slope.
Find slope using `m=(y_2 - y_1)/(x_2 - x_1)`
where `(x_1,y_1)` and `(x_2,y_2)` are the given two points
`(5,1)` and `(0,-6)`:

`m=(-6-1)/(0-5) = (-7)/-5 = 7/5`

You can see this is in both answers.

Now choose either point and plug in to the slope-intercept form of a line: `(y - y_1) = m(x - x_1)`

Choosing the first point results in the first answer and choosing the second point yields the second answer. Also note that the second point is technically the y-intercept, so you could write the equation in slope-intercept form (`y=mx+b`): `y=7/5x-6`.