Transcript § 2.2 Graphing Linear Equations in Two Variables

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§ 2.2 Graphing Linear Equations
in Two Variables
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Determine whether an ordered pair
is a solution of the equation.
5𝑦 − 3𝑥 = 1
Is this point a solution of the linear equation?
8,5
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Determine whether an ordered pair
is a solution of the equation.
5𝑦 − 3𝑥 = 1
Is this point a solution of the linear equation?
8,5
What about the point −3, −2 ?
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Graphing Linear Equations by
Plotting Points
Given an equation, plug in numbers in for x and
solve for the corresponding y value. Basically,
do a “T-table”. Then write the numbers for x
and y as an ordered pair and plot it.
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Graphing Linear Equations by
Plotting Points
Given an equation, plug in numbers in for x and
solve for the corresponding y value. Basically,
do a “T-table”. Then write the numbers for x
and y as an ordered pair and plot it.
E.g.:
𝑦 = −3𝑥 + 4
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Graphing Linear Equations by
Finding Intercepts
 The point where a graph intersects the x-axis
is called the x-intercept.
 The point where a graph intersects the y-axis
is called the y-intercept.
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Graphing Linear Equations by
Finding Intercepts
 The point where a graph intersects the x-axis
is called the x-intercept.
 The point where a graph intersects the y-axis
is called the y-intercept.
 To find the x-intercept, pick y = 0 and solve
for x.
 To find the y-intercept, pick x = 0 and solve
for y.
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Example
 To find the x-intercept, pick y = 0 and solve
for x.
 To find the y-intercept, pick x = 0 and solve
for y.
−3𝑥 = 6𝑦 + 15
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When the Intercept Method “fails.”
There are times when the Intercept Method will
not work so well. It “fails” when (0,0) is a
solution to the equation.
E.g.:
7𝑦 − 8𝑥 = 0
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𝑦=− 𝑥
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Graphing Horizontal and Vertical
Lines
 If an equation only has an x or y variable,
then you have either a horizontal or a vertical
line.
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Graphing Horizontal and Vertical
Lines
 If an equation only has an x or y variable,
then you have either a horizontal or a vertical
line.
E.g.:
x = 3 is a vertical line going through the point
3,0 .
y = 5 is a horizontal line going through the point
0,5 .
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Write each equation in y = b or
x = a. Graph the equations.
1.) −4𝑦 + 3 = −13
2.) −3𝑥 − 5 = 4