Question

Determine the slope for the line that meets each condition stated. Show your work.

a.Passes through the points (3,5) and (−1,−7).
b.Passes through the points given by the table of values.
x y
−2 −7
−1 −6
0 −5
1 −4
2 −3

Answer 1

a. The slope is 3

b. The slope is 1

Explanation:

We can calculate the slope of a line with the following formula:

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

a. Knowing that the line passes through the points (3,5) and (-1,-7), we can identify that:

`y_2=-7\\y_1=5\\\\x_2=-1\\x_1=3`

Then, substituting values into the formula, we get that the slope of this line is:

`m=(-7-5)/(-1-3)\\\\m=(-12)/(-4)\\\\m=3`

b. Choose two points from the table. Let's choose:

`(-2,-7)\\\\(2,-3)`

In this case:

`y_2=-7\\y_1=-3\\\\x_2=-2\\x_1=2`

Then, substituting values into the formula, we get that the slope of this line is:

`m=(-7-(-3))/(-2-2)\\\\m=(-4)/(-4)\\\\m=1`