To find the slope of a line that passes through two points, we use the slope formula:

$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$

where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.

Let's calculate the slope for each pair of points.

(a) Points: $(9, 3)$ and $(19, -17)$

$\text{slope} = \frac{-17 - 3}{19 - 9} = \frac{-20}{10} = -2$

(b) Points: $(-3, 1)$ and $(-17, 2)$

$\text{slope} = \frac{2 - 1}{-17 + 3} = \frac{1}{-14} = -\frac{1}{14}$

(c) Points: $(-20, -4)$ and $(-12, -10)$

$\text{slope} = \frac{-10 + 4}{-12 + 20} = \frac{-6}{8} = -\frac{3}{4}$

(d) Points: $(-19, -6)$ and $(15, 16)$

$\text{slope} = \frac{16 + 6}{15 + 19} = \frac{22}{34} = \frac{11}{17}$

(e) Points: $(-6, 9)$ and $(7, -9)$

$\text{slope} = \frac{-9 - 9}{7 + 6} = \frac{-18}{13} = -\frac{18}{13}$

Final Answers:

• (a) Slope: $-2$
• (b) Slope: $-\frac{1}{14}$
• (c) Slope: $-\frac{3}{4}$
• (d) Slope: $\frac{11}{17}$
• (e) Slope: $-\frac{18}{13}$

Would you like further details on any of these calculations?

Related Questions:

1. How do you calculate the slope if both points lie on the same horizontal line?
2. What does it mean if the slope between two points is zero?
3. How does a negative slope affect the direction of a line?
4. What is the significance of the slope in a linear equation?
5. How do you interpret the slope of a vertical line?

Tip:

Remember that if two points have the same x-coordinate, the line is vertical and the slope is undefined.