Math Snap

STEP 1

1. The slope of a line is calculated using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two distinct points on the line.
2. The slope is a measure of the steepness and direction of a line.
3. A vertical line has an undefined slope.

STEP 2

1. Calculate the slope of Line AB.
2. Calculate the slope of Line CD.
3. Calculate the slope of Line EF.
4. Determine the slope of Line GH.

STEP 3

Identify the coordinates of points A and B for Line AB: $A(2, 3)$ and $B(4, 5)$.

STEP 4

Apply the slope formula:
$$m_{AB} = \frac{5 - 3}{4 - 2} = \frac{2}{2} = 1$$ The slope of Line AB is 1.

STEP 5

Identify the coordinates of points C and D for Line CD: $C(2, 2)$ and $D(6, 0)$.

STEP 6

Apply the slope formula:
$$m_{CD} = \frac{0 - 2}{6 - 2} = \frac{-2}{4} = -\frac{1}{2}$$ The slope of Line CD is $-\frac{1}{2}$.

STEP 7

Identify the coordinates of points E and F for Line EF: $E(0, 0)$ and $F(2, -2)$.

STEP 8

Apply the slope formula:
$$m_{EF} = \frac{-2 - 0}{2 - 0} = \frac{-2}{2} = -1$$ The slope of Line EF is $-1$.

STEP 9

Identify the coordinates of points G and H for Line GH: $G(8, 0)$ and $H(8, 4)$.

Since both points have the same x-coordinate, Line GH is a vertical line.
The slope of a vertical line is undefined.
The slopes of the lines are:
- Line AB: 1
- Line CD: $-\frac{1}{2}$
- Line EF: $-1$
- Line GH: undefined