Finding the Slope Between Two Points

Q1. Find the slope of the line that goes through the points (-7, -7) and (-4, 8).

Background

Topic: Slope of a Line

This question tests your understanding of how to calculate the slope of a line given two points. The slope describes how steep the line is and the direction it goes.

Key Terms and Formula:

• Slope (m): The measure of the steepness of a line.

• Points: $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of two points on the line.

The formula for the slope between two points is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Step-by-Step Guidance

1. Label the points: Let $(-7, -7)$ be $(x_1, y_1)$ and $(-4, 8)$ be $(x_2, y_2)$.

2. Write down the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

3. Substitute the values into the formula: $x_1 = -7$, $y_1 = -7$, $x_2 = -4$, $y_2 = 8$.

4. Calculate the numerator: $y_2 - y_1 = 8 - (-7)$

5. Calculate the denominator: $x_2 - x_1 = -4 - (-7)$

Try solving on your own before revealing the answer!

Final Answer: $m = 5$

$y_2 - y_1 = 8 - (-7) = 15$

$x_2 - x_1 = -4 - (-7) = 3$

$m = \frac{15}{3} = 5$

The slope of the line is 5, which means for every 1 unit you move to the right, the line rises 5 units.