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Algebra 2Lesson 2-2
ALGEBRA 2 LESSON 2-2Linear Equations
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To graph linear equations.
ALGEBRA 2 LESSON 2-2Linear Equations
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ALGEBRA 2 LESSON 2-2Linear Equations
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New VocabularyLinear FunctionLinear Equation
Dependant VariableIndependent Variable
Y-interceptX-Intercept
Slope
Plot the points (0, 2) and (3, –2)
and then draw the line through these two points.
ALGEBRA 2 LESSON 2-2Linear Equations
Graph the equation y = – x + 2.43
If x = 0, then y = 2.
If x = 3, then y = –2.
2-2
ALGEBRA 2 LESSON 2-2Linear Equations
Graph the equation
2-2
xy43
ALGEBRA 2 LESSON 2-2Linear Equations
Graph the equation
2-2
2 yx
ALGEBRA 2 LESSON 2-2Linear Equations
The equation 10x + 5y = 40 models how you can give $.40 change if you have only dimes and nickels. The variable x is the number of dimes, and y is the number of nickels. Graph the equation. Describe the domain and the range. Explain what the x- and y-intercepts represent.
10x + 5y = 40 10x + 5y = 4010x + 5(0) = 40 10(0) + 5y = 40
10x = 40 5y = 40x = 4 y = 8
Set x or y equal to zero to find each intercept.
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The x-intercept is (4, 0), which means that the change can be given using 4 dimes and 0 nickels.
The y-intercept is (0, 8), which means that the change can be given using 0 dimes and 8 nickels.
ALGEBRA 2 LESSON 2-2Linear Equations
(continued)
Use the intercepts to graph the equation.
The number of dimes and the number of nickels must each be a whole number.
The possible solutions for this situation are limited to those points on the line segment connecting (0, 8) and (4, 0) whose x- and y-coordinates are whole numbers.
Therefore, the domain is {0, 1, 2, 3, 4} and the range is {0, 2, 4, 6, 8}.
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ALGEBRA 2 LESSON 2-2Linear Equations
Find the slope of the line through the points (–2, 7) and (8, –6).
Slope = Use the slope formula.y2 –y1
x2 – x1
= Substitute (–2, 7) for (x1, y1) and (8, –6) for (x2, y2).
–6 – 78 – (–2)
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= – Simplify.1310
The slope of the line is – .1310
ALGEBRA 2 LESSON 2-2Linear Equations
Find the slope of the line through the points (–2, -2) and (4, 2).
2-2
ALGEBRA 2 LESSON 2-2Linear Equations
Find the slope of the line through the points (0, -3) and (-9, 6).
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To write equations of lines.
ALGEBRA 2 LESSON 2-2Linear Equations
1-1
ALGEBRA 2 LESSON 2-2Linear Equations
1-1
Standard Form of a Linear Equation
CByAx
ALGEBRA 2 LESSON 2-2Linear Equations
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Point-Slope Form of a Linear Equation
11 xxmyy
ALGEBRA 2 LESSON 2-2Linear Equations
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Slope-Intercept Form of a Linear Equation
bmxy
ALGEBRA 2 LESSON 2-2Linear Equations
Write in standard form an equation of the line with slope 3 through the point (–1, 5).
y – y1 = m(x – x1) Use the point-slope equation.
y – 5 = 3[x – (–1)] Substitute 3 for m, 5 for y1, and –1 for x1.
y – 5 = 3[(x + 1)] Simplify.
y – 5 = 3x + 3 Distributive Property
3x – y = –8 Write in standard form.
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ALGEBRA 2 LESSON 2-2Linear Equations
Write in standard form an equation of the line with slope 2 through the point (4, -2).
2-2
ALGEBRA 2 LESSON 2-2Linear Equations
Write in standard form an equation of the line with slope 5/6 through the point (5, 6).
2-2
ALGEBRA 2 LESSON 2-2Linear Equations
Write in point-slope form an equation of the line through (4, –3) and (5, –1).
y – y1 = m(x – x1) Write the point-slope equation.
y + 3 = 2(x – 4) Simplify.
You can also use (5, –1) for (x1, y1) and (4, –3) for (x2, y2).
This gives the equation y + 1 = 2(x – 5). Both equations define the same line.
y – y1 = (x – x1) Substitute the slope formula for m.y2 – y1
x2 – x1
y – (–3) = (x – 4) Substitute: x1 = 4, y1 = –3, x2 = 5, y2 = –1.–1 – (–3)5 – 4
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ALGEBRA 2 LESSON 2-2Linear Equations
Write in point-slope form an equation of the line through (5, 0) and (-3, 2).
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ALGEBRA 2 LESSON 2-2Linear Equations
Write in point-slope form an equation of the line through (-2, -1) and (-10, 17).
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ALGEBRA 2 LESSON 2-2Linear Equations
Find the slope of –7x + 2y = 8.
–7x + 2y = 8 Add 7x to both sides.
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y = x + 4 Write in the slope-intercept form.72
The slope of the line is .72
ALGEBRA 2 LESSON 2-2Linear Equations
Find the slope of
2-2
123 yx
ALGEBRA 2 LESSON 2-2Linear Equations
Find the slope of
2-2
121
32
yx
ALGEBRA 2 LESSON 2-2Linear Equations
Write an equation of the line in slope-intercept form through (5, –3) and perpendicular to y = 4x + 1. Graph both lines.
2-2
m = – Find the negative reciprocal of 4.14
y = mx + b Use slope-intercept form.
y = – x + b Slope is – .14
14
14–3 = – (5) + b Substitute (5, –3) for (x, y).
–3 = – + b Simplify.54
– = b Solve for b.74
y = – x – Write the equation.14
74
ALGEBRA 2 LESSON 2-2Linear Equations
Write an equation in slope-intercept form of the line through (-1, 3) and perpendicular to y = 5x-3. Graph both lines.
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ALGEBRA 2 LESSON 2-2Linear Equations
Write an equation in slope-intercept form of the line through (0, 4) and perpendicular to y = 3/4x + 2. Graph both lines.
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Algebra 2Lesson 2-2(Page 62)
ALGEBRA 2 LESSON 2-2Linear Equations
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