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Lesson Plans and Worksheets for Grade 8

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More Lessons for Grade 8

Common Core For Grade 8

Videos, examples, and solutions to help Grade 8 students learn how to graph equations in the form of y = mx + b using information about slope and y-intercept.

### New York State Common Core Math Grade 8, Module 4, Lesson 18

### Lesson 18 Student Outcomes

• Students graph equations in the form of y = mx + b using information about slope and y-intercept.

• Students know that if they have two straight lines with the same slope and a common point that the lines are the same.

### Lesson 18 Summary

• The equation y = mx + b is in slope-intercept form. The number m represents the slope of the graph and the point (0,b) is the location where the graph of the line intersects the y-axis.

• To graph a line from the slope-intercept form of a linear equation, begin with the known point, (0, b), then use the slope to find a second point. Connect the points to graph the equation.

• There is only one line passing through a given point with a given slope.

Lesson 18 Opening Exercise

Examine each of the graphs and their equations below. Identify the coordinates of the point where the line intersects the y-axis. Describe the relationship between the point and the equation y = mx + b.

Standard Form of a linear equation: ax + by + c = 0

Slope-Intercept Form of a linear equation: y = mx + b

Example 1

Graph the equation y = 2/3 x + 1. Name the slope and y-intercept.

Example 2

Graph the equation y = -3/4 x - 2. Name the slope and y-intercept.

Example 3

Graph the equation y = 4x - 7. Name the slope and y-intercept.

Exercises 1–4

1. Graph the equation y = 5/2 x - 4.

a. Name the slope and y-intercept.

b. Graph the known point, then use the slope to find a second point before drawing the line.

2. Graph the equation y = -3x + 6.

a. Name the slope and y-intercept.

b. Graph the known point, then use the slope to find a second point before drawing the line.

3. The equation y = 1x simplifies to y = x. Graph the equation y = x.

a. Name the slope and y-intercept.

b. Graph the known point, then use the slope to find a second point before drawing the line.

4. Graph the point (0, 2).

a. Find another point on the graph using the slope, m = 2/7.

b. Connect the points to make the line.

c. Draw a different line that goes through the point (0, 2) with slope 2/7. What do you notice?

Exercises 5–6

5. A bank put $10 into a savings account when you opened the account. Eight weeks later you have a total of $24. Assume you saved the same amount every week.

a. If y is the total amount of money in the savings account and x represents the number of weeks, write an equation in the form y = mx + b that describes the situation.

b. Identify the slope and the y-intercept. What do these numbers represent?

c. Graph the equation on a coordinate plane.

d. Could any other line represent this situation? For example, could a line through point (0, 100 with slope 7/5 represent the amount of money you save each week? Explain.

6. A group of friends are on a road trip. So far they have driven 120 miles. They continue their trip and drive at a constant rate of 50 miles per hour.

a. Let y represent the total distance traveled in x hours. Write an equation to represent the total number of miles driven in x hours.

b. Identify the slope and the y-intercept. What do these numbers represent?

c. Graph the equation on a coordinate plane.

d. Could any other line represent this situation? For example, could a line through point (0, 120) with slope 75 represent the total distance the friends drive? Explain.

Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Videos, examples, and solutions to help Grade 8 students learn how to graph equations in the form of y = mx + b using information about slope and y-intercept.

Download Worksheets for Grade 8, Module 4, Lesson 18

• Students know that if they have two straight lines with the same slope and a common point that the lines are the same.

• The equation y = mx + b is in slope-intercept form. The number m represents the slope of the graph and the point (0,b) is the location where the graph of the line intersects the y-axis.

• To graph a line from the slope-intercept form of a linear equation, begin with the known point, (0, b), then use the slope to find a second point. Connect the points to graph the equation.

• There is only one line passing through a given point with a given slope.

Lesson 18 Opening Exercise

Examine each of the graphs and their equations below. Identify the coordinates of the point where the line intersects the y-axis. Describe the relationship between the point and the equation y = mx + b.

Standard Form of a linear equation: ax + by + c = 0

Slope-Intercept Form of a linear equation: y = mx + b

Example 1

Graph the equation y = 2/3 x + 1. Name the slope and y-intercept.

Example 2

Graph the equation y = -3/4 x - 2. Name the slope and y-intercept.

Example 3

Graph the equation y = 4x - 7. Name the slope and y-intercept.

1. Graph the equation y = 5/2 x - 4.

a. Name the slope and y-intercept.

b. Graph the known point, then use the slope to find a second point before drawing the line.

2. Graph the equation y = -3x + 6.

a. Name the slope and y-intercept.

b. Graph the known point, then use the slope to find a second point before drawing the line.

3. The equation y = 1x simplifies to y = x. Graph the equation y = x.

a. Name the slope and y-intercept.

b. Graph the known point, then use the slope to find a second point before drawing the line.

4. Graph the point (0, 2).

a. Find another point on the graph using the slope, m = 2/7.

b. Connect the points to make the line.

c. Draw a different line that goes through the point (0, 2) with slope 2/7. What do you notice?

Exercises 5–6

5. A bank put $10 into a savings account when you opened the account. Eight weeks later you have a total of $24. Assume you saved the same amount every week.

a. If y is the total amount of money in the savings account and x represents the number of weeks, write an equation in the form y = mx + b that describes the situation.

b. Identify the slope and the y-intercept. What do these numbers represent?

c. Graph the equation on a coordinate plane.

d. Could any other line represent this situation? For example, could a line through point (0, 100 with slope 7/5 represent the amount of money you save each week? Explain.

6. A group of friends are on a road trip. So far they have driven 120 miles. They continue their trip and drive at a constant rate of 50 miles per hour.

a. Let y represent the total distance traveled in x hours. Write an equation to represent the total number of miles driven in x hours.

b. Identify the slope and the y-intercept. What do these numbers represent?

c. Graph the equation on a coordinate plane.

d. Could any other line represent this situation? For example, could a line through point (0, 120) with slope 75 represent the total distance the friends drive? Explain.

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