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2.3 Quick Graphs of Linear Equations
Algebra 2
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Slope-Intercept Form Slope intercept form: y=mx+b m=slope
b=y-intercept (where the graph intersects the y-axis)
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Graphing Equations in Slope-Intercept Form
Write the equation in slope-intercept form Graph the y-intercept Use slope to βrise and runβ to another point Draw a line through the points
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Example Graph π¦= 1 2 π₯+1
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Example To buy a $1200 stereo, you pay a $200 deposit and then make weekly payments according to the equation π=1000β40π‘, where a is the amount you owe and t is the number of weeks. How much do you owe originally? What is your weekly payment? Graph the model.
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example The number of gallons g of water in your storage tank is given by π=500β20π‘, with t in days. Using a graph, find the daily rate of water use, and determine in home many days the tank will become empty.
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Standard Form Standard form: Ax + By = C ; where A and B are not zero
x-intercept: where the line intersects the x-axis
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Graphing Equations in Standard Form
Write the equation in standard form Find the x-intercept by making y=0 and solving for x. Graph the x-intercept. Find the y-intercept by making x=0 and solving for y. Graph the y-intercept. Draw a line through the points
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Examples Graph 3π₯β2π¦=6 using standard form. Then rewrite the equation in slope-intercept form. Graph 2π₯+5π¦=10 using standard form.
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Horizontal and Vertical Lines
Horizontal Lines: The graph of π¦=π is a horizontal line through (0, c) Vertical Lines: The graph of π₯=π is a vertical line through (c, 0)
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Example Graph the following equations π¦=β2 π₯=3 π¦=1 π₯=β1
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Example Students are selling tickets to a school play. The goal is to raise $600. Tickets are $4 for adults and $3 for students. Describe the numbers of adult and student tickets sold that will reach the goal.
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Example If x represents the number of 4 in high bricks and y is the number of 6 in bricks it takes to reach the top of a 60 in wall, what are the endpoint of the segment containing the numbers of 4 in and 6in bricks that will reach the top?
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