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Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

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ALGEBRA 2 LESSON 2-2 Linear Equations 1-1 New Vocabulary Linear Function Linear Equation Dependant Variable Independent Variable Y-intercept X-Intercept Slope
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Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1
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Page 1: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

Algebra 2Lesson 2-2

ALGEBRA 2 LESSON 2-2Linear Equations

1-1

Page 2: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

To graph linear equations.

ALGEBRA 2 LESSON 2-2Linear Equations

1-1

Page 3: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

ALGEBRA 2 LESSON 2-2Linear Equations

1-1

New VocabularyLinear FunctionLinear Equation

Dependant VariableIndependent Variable

Y-interceptX-Intercept

Slope

Page 4: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

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

Page 5: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

ALGEBRA 2 LESSON 2-2Linear Equations

Graph the equation

2-2

xy43

Page 6: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

ALGEBRA 2 LESSON 2-2Linear Equations

Graph the equation

2-2

2 yx

Page 7: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

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.

2-2

Page 8: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

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}.

2-2

Page 9: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

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)

2-2

= – Simplify.1310

The slope of the line is – .1310

Page 10: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

ALGEBRA 2 LESSON 2-2Linear Equations

Find the slope of the line through the points (–2, -2) and (4, 2).

2-2

Page 11: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

ALGEBRA 2 LESSON 2-2Linear Equations

Find the slope of the line through the points (0, -3) and (-9, 6).

2-2

Page 12: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

To write equations of lines.

ALGEBRA 2 LESSON 2-2Linear Equations

1-1

Page 13: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

ALGEBRA 2 LESSON 2-2Linear Equations

1-1

Standard Form of a Linear Equation

CByAx

Page 14: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

ALGEBRA 2 LESSON 2-2Linear Equations

1-1

Point-Slope Form of a Linear Equation

11 xxmyy

Page 15: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

ALGEBRA 2 LESSON 2-2Linear Equations

1-1

Slope-Intercept Form of a Linear Equation

bmxy

Page 16: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

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.

2-2

Page 17: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

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

Page 18: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

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

Page 19: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

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

2-2

Page 20: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

ALGEBRA 2 LESSON 2-2Linear Equations

Write in point-slope form an equation of the line through (5, 0) and (-3, 2).

2-2

Page 21: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

ALGEBRA 2 LESSON 2-2Linear Equations

Write in point-slope form an equation of the line through (-2, -1) and (-10, 17).

2-2

Page 22: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

ALGEBRA 2 LESSON 2-2Linear Equations

Find the slope of –7x + 2y = 8.

–7x + 2y = 8 Add 7x to both sides.

2-2

y = x + 4 Write in the slope-intercept form.72

The slope of the line is .72

Page 23: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

ALGEBRA 2 LESSON 2-2Linear Equations

Find the slope of

2-2

123 yx

Page 24: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

ALGEBRA 2 LESSON 2-2Linear Equations

Find the slope of

2-2

121

32

yx

Page 25: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

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

Page 26: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

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.

2-2

Page 27: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

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.

2-2

Page 28: Algebra 2 Lesson 2-2 ALGEBRA 2 LESSON 2-2 Linear Equations 1-1.

Algebra 2Lesson 2-2(Page 62)

ALGEBRA 2 LESSON 2-2Linear Equations

1-1


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