Question

QUESTION 9 1 POINT Find the equation of a line that contains the points (-2,-5) and (3, -1). Write the equation in slope-intercept form, using fractions when required Provide your answer below​

Answer 1

If only slope:

`y = (4)/(5)x + b`

If slope and y-intercept:

`y = (4)/(5)x - 6.6\\or\\y = (4)/(5)x - 3.4`

*both are correct answers see steps below*

Explanation:

The equation to find the slope is
`(y_(2) - y_(1))/(x_(2) - x_(1))`.

The equation for slope-intercept form is
`y = mx + b`.

First, find the slope between two points.

`(-1 - (-5))/(3 - (-2)) = (4)/(5)`

Keep the difference as a fraction if it can't be divided.

Next, plug in the slope value into the equation.

`y = (4)/(5)x + b`

If you also need to find what b is, pick a point; (-2, -5) OR (3, -1). Then fill in the equation with it's x and y values. (I'll do both points to show two different results).

Point (-2, -5):

`(-5) = (4)/(5)(-2) + b`

`(-5) = (-1.6) + b`

Add 1.6 on both sides to isolate the b. (since -1.6 is a negative, we need to cancel it out with its opposite)

`b = -6.6`

Point (3, -1):

`(-1) = (4)/(5)(3) + b`

`(-1) = (2.4) + b`

Subtract 2.4 on both sides to isolate the b. (since 2.4 is a positive, we need to cancel it out with its opposite)

`b = -3.4`

It does mean that both slopes have different y-intercepts but it overly depends on the point. These steps will ensure you to the correct answer.