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Transcript of Review Videos Graphing the x and y intercept Graphing the x and y intercepts Graphing a line in...
Review Videos
• Graphing the x and y intercept• Graphing the x and y intercepts• Graphing a line in slope intercept form• Converting into slope intercept form
Chapter 7 Section 6
Families of Linear Graphs
What You’ll Learn
You’ll learn to explore the effects of changing the slopes and y-intercepts of linear
functions.
Why It’s Important
BusinessFamilies of graphs can display different fees.
Families of linear graphs often fall into two categories-
1.Those with the same slope
2. Those with the same y-intercept.
Family of Graphs
y = ½x + 3
y = ½x - 1
Same Slope
What do these lineshave in common?
Family of Graphs
y = ⅓x + 1y = -x + 1
Same y-intercept
What do these lineshave in common?
Not a Family of Graphs
y = ⅓x
y = x + 2
Differenty-intercept and slope
What do these lineshave in common?
Example 1Graph each pair of equations. Describe any similarities or
differences. Explain why they are a family of graphs.y = 3x + 4y = 3x – 2The graphs have y-intercepts of 4 and -2, respectively.
They are a family of graphs because the slope of each line is 3.
y = 3x + 4
y = 3x - 2
Example 2Graph each pair of equations. Describe any similarities or
differences. Explain why they are a family of graphs.y = x + 3y = -½x + 3Each graph has a different slope.
Each graph has a y-intercept of 3.Thus, they are a family of graphs. y = x + 3
y = -½x + 3
Hint:
You can compare graphs of lines by looking at their equations.
Example 3• Matthew and Juan are starting their own pet care business. Juan wants to
charge $5 an hour. Matthew thinks they should charge $3 an hour. Suppose x represents the number of hours. Then y = 5x and y = 3x represents how much they would charge, respectively. Compare and contrast the graphs of the equations.
The equations have the same y-intercept, but the graph of y = 5x is steeper. This is because its slope, which represents $5 per hour, is greater that the slope of the graph of y = 3x.
6
5
4
3
2
01 1.5.5 2
y = 5x
y = 3x
Your Turn
Compare and contrast the graphs of the equations. Verify by graphing the equation.
y = -3x + 4y = -x + 4
Answer
y = -3x + 4y = -x + 4
Same y-intercept Different slope y = -3x + 4
y = -x + 4
Try This One
Compare and contrast the graphs of the equations. Verify by graphing the equation.
y = ⅔x + 3y = ⅔x -1
Answer
y = ⅔x + 3y = ⅔x -1
Same slope Different y-intercept y = ⅔x - 1
y = ⅔x + 3
Parent Graph
A parent graph is the simplest of the graphs in a family. Let’s summarize how changing the m or b in y = mx + b affects the
graph of the equation. Parent: y = x
y = xy = 3x
y = ¼x
As the value of m Increases, the line Gets steeper
Parent: y = -x
y = -xy = -3x
y = -¼xAs the value of m Decreases, the line Gets steeper.
Parent: y = 2x
y = 2x
y = 2x + 3y = 2x - 4
As the value of b Increases, the graph shifts Up on the y-axis. As the value of b decreases,the graph shifts down on the y-axis
You can change a graph by changing the slope or y-intercept.
Example 4
Change y = -½x + 3 so that the graph of the new equation fits each description.
Same y-intercept, steeper negative slopeThe y-intercept is 3, and the slope is -½. The new equation will also have a y-interceptof 3. In order for the slope to be steeper and still be negative, its value must be lessthan -½, such as -2. The new equation is y = -2x + 3.
y = -2x + 3
y = -½x + 3
Example 5
Change y = -½x + 3 so that the graph of the new equation fits each description.
Same slope, y-intercept is shifted up 4 unitsThe slope of the new equation will be -½. Since the current y-intercept will be 3 + 4 or 7.The new equation is y = -½x + 7. Always check by graphing
y = -½x + 7
y = -½x + 3
Your Turn
Change y = 2x + 1 so that the graph of the new equation fits each description.
Same slope, shifteddown 1 unit.
y = 2x + 0 Simplified to y = 2x
Your Turn
Change y = 2x + 1 so that the graph of the new equation fits each description.
Same y-intercept, less steep positive slope
y = x + 1