Question

Calculate the slope of the line that passes through the labeled points on the graph.

Answer 1

m=(Y2-Y1)/(X2-X1)

(1.) m=(2-(-1))/(-2-3) = 3/-5 = -3/5

(2.) m=(-2-1)/(-3-2) = -3/-5 = 3/5

(3.) m=Infinity (equation: x=-2)

Answer 2

The slopes of the lines passing through the given points are: 1.
`\((-2,2)\)` and
`\((3,-1)\)`:
`\(m = -(3)/(5)\)`. 2.
`\((-3,-2)\)` and
`\((2,1)\)`:
`\(m = (3)/(5)\)`. 3.
`\((-2,-2)\)` and
`\((-2,3)\)`: The slope is undefined (vertical line).

To calculate the slope m of a line given two points
`\((x_1, y_1)\)` and
`\((x_2, y_2)\)`, you can use the formula:

`\[m = (y_2 - y_1)/(x_2 - x_1)\]`

Let's apply this formula to the given points:

1. For points (-2,2) and (3,-1):

`\[m = (-1 - 2)/(3 - (-2)) = (-3)/(5)\]`

2. For points (-3,-2) and (2,1):

`\[m = (1 - (-2))/(2 - (-3)) = (3)/(5)\]`

3. For points (-2,-2) and (-2,3):

`\[m = (3 - (-2))/((-2) - (-2)) = (5)/(0)\]`

The slope for the third set of points is undefined because the denominator becomes zero, indicating a vertical line. The first two sets of points have slopes of
`\(-(3)/(5)\)` and
`\((3)/(5)\)` respectively.