Math: Finding Slope of Points and Graphs

What is the slope of the line that contains the points (10, -1) and (-8, 6)?

Based on the cost table, what is the cost per person when there are 4 people?

Using the distance table, how far does your car travel in one hour?

What is the slope of the line represented by the points (0, -2) and (3, 4)?

What does the slope of 1/40 represent in the context of the cost table?

Slope Calculation from Points

Slope (m) measures the steepness of a line connecting two points.
Formula for slope: m = (y2 - y1) / (x2 - x1).
Example points: (10, -1) and (-8, 6).
Substitute the coordinates in the formula to find the slope.

Example with Given Points

Points labeled as (x1, y1) = (0, -2) and (x2, y2) = (3, 4).
Calculation: m = (4 - (-2)) / (3 - 0) = 6 / 3 = 2.

Slope Calculation from Tables

Slope can also be determined from a table of values.
Example table for ski rentals:
- Shows cost associated with varying numbers of people.
- Slope derived from changes in cost relative to the number of people.
Example table for driving distance:
- Displays miles driven over different time intervals.
- Slope represents miles per hour based on time and distance data.

Key Concepts in Calculating Slope from Tables

Identifying consistent increments in table values.
Slope determination from given cost per person in the ski rental example.
Per-hour travel rate derived from distance and time in the driving distance example.
The significance of understanding slope in practical contexts like rental costs and travel distances.

This quiz focuses on calculating the slope of a line using given points, tables, and graphs. Test your understanding of the formula for slope and how to apply it to different scenarios. Challenge yourself with multiple-choice questions based on the slope concept.