Question

Write the equation of the line that passes through the points (-1, 2) and (6, 3) in slope- intercept form.

Choose (x1, y1) = (-1,2)

Step 2. x2 = ? y2 = ?

Answer 1

y =
`(-1)/(6)`x +
`(27)/(7)`

Explanation:

(-1,2) (6,3)

y = mx + b

To write the equation, we need two things. We need the slope (m) and the y-intercept (b). We will use the two points given to do this.

Slope

Slope is the change in y over the change in x. We find the change by subtracting. From the points given, the y values are 3 and 2. From the points give, the x values are 6 and -1

`(3-2)/(6 - -1)` =
`(1)/(6+1)` =
`(-1)/(7)`

The slope (m) is
`(-1)/(7)`

y-intercept

to find the y-intercept we need the slope
`(-1)/(7)` and one of the two points given. It does not matter which point we use. I am going to use (6,3) because I would rather deal with positive numbers

We are going to us the x value of 6 and the y value to 3 and plug it into our slope intercept equation to solve for b

y = mx + b

3 =
`(-1)/(7)`(6) + b

3 =
`(-6)/(7)` + b Add
`(6)/(7)` to both sides

3 +
`(6)/(7)` = b

`(3)/(1)` +
`(6)/(7)` = b

`(21)/(7)` +
`(6)/(7)` = b

`(27)/(7)` = b

The y-intercept is
`(27)/(7)`.

Now that we have the slope or m (
`(-1)/(6)`) and the y-intercept or b (
`(27)/(7)`) we can write the equation

y = mx + b

y =
`(-1)/(6)`x +
`(27)/(7)`

Helping in the name of Jesus.