Question

How do you write an equation in SLOPE-INTERCEPT form of the line passing through the given points (2, 7), (1, -4)?

Answer 1

`y=11x-15`

Explanation:

The slope-intercept form is `y=mx+c`, where `m` is the slope and `c` is the `y`-intercept.

The slope is given by the change in `y` divided by the change in `x`,

`(y_2-y_1)/(x_2-x_1)=(-4-7)/(1-2)=11`

which gives us

`y=11x+c`.

Now substitute in values for `x` and `y` from the points given to find `c`.

`-4_y=11*1_x+c`
`c=-15`

and put this back into the equation

`y=11x-15`

Answer 2

`y = 11x - 15`

Explanation:

Slope intercept formula: `y = mx + b`
1) find the slope of the two points by using the formula:
`(y_2 - y_1)/(x_2 - x_1) = (-4 - 7)/(1 - 2) = (-11)/-1 = 11`

We now have so far: `y = 11x + b`

We can use a sample coordinate to find the value of b or the y-intercept (the place where the line crosses the y-axis).

We can use (2,7) where `7 = y` and `2 = x`.
`7 = 11(2) + b`

Solve for b.
`7 = 11(2) + b`
`7 = 22 + b`
`7 - 22 = 22 -22 + b`
`-15 = b`

Slope-intercept form: `y = 11x - 15`