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Graph Equations using Slope and Intercept




 

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


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Common Core For Grade 8

New York State Common Core Math Module 4, Grade 8, 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.





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