The Graph y = mx + c has Slope m

Video Solutions to help Grade 6 students learn the slope of a line joining any two distinct points of the graph of y = mx + c has slope, m

New York State Common Core Math Module 4, Grade 8, Lesson 17

Lesson 17 Student Outcomes

• Students show that the slope of a line joining any two distinct points of the graph of y = mx + c has slope, m.
• Students transform the standard form of an equation into y = - a/b x + c/b.

Lesson 17 Summary

The line joining two distinct points of the graph of the linear equation y = mx + b has slope m. The m of y = mx + b is the number that describes the slope. For example, in the equation y = -2x + 4 the slope of the graph of the line is -2.

Lesson 17 Classwork

Exercises
1. Find at least three solutions to the equation y = 2x, and graph the solutions as points on the coordinate plane. Connect the points to make a line. Find the slope of the line.

2. Find at least three solutions to the equation y = 3x - 1, and graph the solutions as points on the coordinate plane. Connect the points to make a line. Find the slope of the line.

3. Find at least three solutions to the equation y = 3x + 1, and graph the solutions as points on the coordinate plane. Connect the points to make a line. Find the slope of the line.

4. The graph of the equation y = 7x - 3 has what slope?

5. The graph of the equation y = -3/4 x - 3 has what slope?

6. You have \$20 in savings at the bank. Each week, you add \$2 to your savings. Let y represent the total amount of money you have saved at the end of weeks. Write an equation to represent this situation and identify the slope of the equation. What does that number represent?

7. A friend is training for a marathon. She can run 4 miles in 28 minutes. Assume she runs at a constant rate. Write an equation to represent the total distance, y, your friend can run in minutes. Identify the slope of the equation. What does that number represent?

8. Four boxes of pencils cost \$5. Write an equation that represents the total cost, y, for x boxes of pencils. What is the slope of the equation? What does that number represent?

9. Solve the following equation for y: 9x - 3y = 15, then identify the slope of the line.

10. Solve the following equation for y: 5x + 9y = 6, then identify the slope of the line.

11. Solve the following equation for y: ax + by = c, then identify the slope of the line.