Question

find the slope of the line.
4.
7.
graph the data. then find and interpret

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Solve for problem 4 (points (0,0) and (1,4))

Substitute \( x_1 = 0, y_1 = 0, x_2 = 1, y_2 = 4 \) into the formula:
\( m = \frac{4 - 0}{1 - 0} = \frac{4}{1} = 4 \).

Step3: Solve for problem 5 (points (0,0) and (2,3))

Substitute \( x_1 = 0, y_1 = 0, x_2 = 2, y_2 = 3 \):
\( m = \frac{3 - 0}{2 - 0} = \frac{3}{2} \).

Step4: Solve for problem 6 (points (3,2) and (6,3))

Substitute \( x_1 = 3, y_1 = 2, x_2 = 6, y_2 = 3 \):
\( m = \frac{3 - 2}{6 - 3} = \frac{1}{3} \).

Step5: Solve for problem 7 (points (-4,-1) and (1,4))

Substitute \( x_1 = -4, y_1 = -1, x_2 = 1, y_2 = 4 \):
\( m = \frac{4 - (-1)}{1 - (-4)} = \frac{5}{5} = 1 \).

Step6: Solve for problem 8 (points (-4,-3) and (2,1.5))

Substitute \( x_1 = -4, y_1 = -3, x_2 = 2, y_2 = 1.5 \):
\( m = \frac{1.5 - (-3)}{2 - (-4)} = \frac{4.5}{6} = 0.75 \) (or \( \frac{3}{4} \)).

Step7: Solve for problem 9 (points (4,1.2) and (10,6))

Substitute \( x_1 = 4, y_1 = 1.2, x_2 = 10, y_2 = 6 \):
\( m = \frac{6 - 1.2}{10 - 4} = \frac{4.8}{6} = 0.8 \) (or \( \frac{4}{5} \)).

Answer:

• Problem 4: Slope = \( 4 \)
• Problem 5: Slope = \( \frac{3}{2} \)
• Problem 6: Slope = \( \frac{1}{3} \)
• Problem 7: Slope = \( 1 \)
• Problem 8: Slope = \( \frac{3}{4} \) (or \( 0.75 \))
• Problem 9: Slope = \( \frac{4}{5} \) (or \( 0.8 \))