Question

page 2
part 4 - find slope from two points (using graph)
(-2, 3) and (4, 6)
(5, -1) and (-1, 4)
(-3, 4) and (2, 4)
(3, -2) and (3, 5)
for each pair of points, there is a graph (grid with axes) and a slope formula ( m = \frac{rise}{run} ) (or just ( m = )) to fill in.
part 5 - find slope using slope formula

1. (15, -10) and (-5, 6) ( m = )
2. (-18, 7) and (4, 7) ( m = ) (with -18 written on the left)
3. (-9, -12) and (-9, 3) ( m = )
4. (-12, -3) and (8, 9) ( m = )

Explanation:

Part 4 - First Pair (-2,3) and (4,6)

Step1: Find Rise and Run

Rise is change in y: \( 6 - 3 = 3 \). Run is change in x: \( 4 - (-2) = 6 \).

Step2: Calculate Slope

\( m=\frac{\text{rise}}{\text{run}}=\frac{3}{6}=\frac{1}{2} \).

Part 4 - Second Pair (5,-1) and (-1,4)

Step1: Find Rise and Run

Rise: \( 4 - (-1) = 5 \). Run: \( -1 - 5 = -6 \).

Step2: Calculate Slope

\( m=\frac{\text{rise}}{\text{run}}=\frac{5}{-6}=-\frac{5}{6} \).

Part 4 - Third Pair (-3,4) and (2,4)

Step1: Find Rise and Run

Rise: \( 4 - 4 = 0 \). Run: \( 2 - (-3) = 5 \).

Step2: Calculate Slope

\( m=\frac{0}{5}=0 \).

Part 4 - Fourth Pair (3,-2) and (3,5)

Step1: Find Rise and Run

Rise: \( 5 - (-2) = 7 \). Run: \( 3 - 3 = 0 \) (undefined as division by zero).

Step2: Calculate Slope

\( m \) is undefined (vertical line).

Part 5 - First Pair (15,-10) and (-5,6)

Step1: Slope Formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \)

Substitute: \( y_2=6, y_1=-10, x_2=-5, x_1=15 \).

Step2: Calculate

\( m=\frac{6 - (-10)}{-5 - 15}=\frac{16}{-20}=-\frac{4}{5} \).

Part 5 - Second Pair (-18,7) and (4,7)

Step1: Slope Formula

Substitute: \( y_2=7, y_1=7, x_2=4, x_1=-18 \).

Step2: Calculate

\( m=\frac{7 - 7}{4 - (-18)}=\frac{0}{22}=0 \).

Part 5 - Third Pair (-9,-12) and (-9,3)

Step1: Slope Formula

Substitute: \( y_2=3, y_1=-12, x_2=-9, x_1=-9 \).

Step2: Calculate

\( m=\frac{3 - (-12)}{-9 - (-9)}=\frac{15}{0} \) (undefined).

Part 5 - Fourth Pair (-12,-3) and (8,9)

Step1: Slope Formula

Substitute: \( y_2=9, y_1=-3, x_2=8, x_1=-12 \).

Step2: Calculate

\( m=\frac{9 - (-3)}{8 - (-12)}=\frac{12}{20}=\frac{3}{5} \).

Answer:

Part 4:

1. \( \frac{1}{2} \)
2. \( -\frac{5}{6} \)
3. \( 0 \)
4. Undefined

Part 5:

1. \( -\frac{4}{5} \)
2. \( 0 \)
3. Undefined
4. \( \frac{3}{5} \)