Question

independent practice
find the slope of a ski run that descends 15 feet for every horizontal change of 24 feet.
find the slope of each line.
2.
3.
the points given in the table lie on a line. find the slope of each line.
4.

x	y
2	4
4	-1
6	-6

5.

x	y
1	5
2	7
3	9

Explanation:

Problem 1: Ski Run Slope

Step1: Recall slope formula

Slope $m = \frac{\text{vertical change}}{\text{horizontal change}}$. Here, vertical change (descend) is $-15$ ft (negative for descent), horizontal change is $24$ ft.
$m = \frac{-15}{24}$

Step2: Simplify the fraction

Divide numerator and denominator by GCD(15,24)=3:
$m = \frac{-15 \div 3}{24 \div 3} = \frac{-5}{8}$

Problem 3: Graph Line Slope

Step1: Identify two points on the line

From the graph, let's take points $(0, -1)$ and $(1, 0)$ (or other clear points).

Step2: Apply slope formula

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-1)}{1 - 0} = \frac{1}{1} = 1$

Problem 5: Table of Points Slope

Step1: Select two points from the table

Let’s use $(0, 3)$ and $(1, 5)$.

Step2: Calculate slope

$m = \frac{5 - 3}{1 - 0} = \frac{2}{1} = 2$

Problem 4: Table of Points Slope

Answer:

s:

1. $\boldsymbol{-\frac{5}{8}}$
2. $\boldsymbol{\frac{1}{2}}$ (or other correct value based on exact graph points)
3. $\boldsymbol{1}$
4. $\boldsymbol{-\frac{5}{2}}$ (or $-2.5$)
5. $\boldsymbol{2}$