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Linear Functions PowerPoint PPT Presentation


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Linear Functions. Review of Formulas. Formula for Slope. Standard Form. *where A>0 and A, B, C are integers. Slope-intercept Form. Point-Slope Form. Find the slope of a line through points (3, 4) and (-1, 6). Change into standard form . .

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Linear Functions

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Linear functions l.jpg

Linear Functions


Review of formulas l.jpg

Review of Formulas

Formula for Slope

Standard Form

*where A>0 and A, B, C are integers

Slope-intercept Form

Point-Slope Form


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Find the slope of a line through points (3, 4) and (-1, 6).


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Change into standard form.


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Change into slope-intercept form and identify the slope and y-intercept.


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Write an equation for the line that passes through (-2, 5) and (1, 7):

Find the slope:

Use point-slope form:


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x-intercepts and y-intercepts

The intercept is the point(s) where the graph crosses the axis.

To find an intercept, set the other variable equal to zero.


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Horizontal Lines

  • Slope is zero.

  • Equation form is y = #.

  • Write an equation of a line and graph it with zero slope and y-intercept of -2.

  • y = -2

  • Write an equation of a line and graph it that passes through (2, 4) and (-3, 4).

    • y = 4


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Vertical Lines

  • Slope is undefined.

  • Equation form is x = #.

  • Write an equation of a line and graph it with undefined slope and passes through (1, 0).

  • x = 1

  • Write an equation of a line that passes through (3, 5) and (3, -2).

    • x = 3


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  • Graphing Lines

    *You need at least 2 points to

    graph a line.

    Using x and y intercepts:

    • Find the x and y intercepts

    • Plot the points

    • Draw your line


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Graph using x and y intercepts

2x – 3y = -12

x-intercept

2x = -12

x = -6

(-6, 0)

y-intercept

-3y = -12

y = 4

(0, 4)


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Graph using x and y intercepts

6x + 9y = 18

x-intercept

6x = 18

x = 3

(3, 0)

y-intercept

9y = 18

y = 2

(0, 2)


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  • Graphing Lines

    Using slope-intercept form y = mx + b:

    • Change the equation to y = mx + b.

    • Plot the y-intercept.

    • Use the numerator of the slope to count the

    • corresponding number of spaces up/down.

    • Use the denominator of the slope to count the corresponding number of spaces left/right.

    • Draw your line.


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Slope

m = -4 = -4

1

y-intercept

(0, 1)

Graph using slope-intercept form y = -4x + 1:


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Slope

m = 3

4

y-intercept

(0, -2)

Graph using slope-intercept form

3x - 4y = 8

y = 3x - 2

4


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  • Parallel Lines

  • **Parallel lines have the same slopes.

  • Find the slope of the original line.

  • Use that slope to graph your new line and to write the equation of your new line.


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Graph a line parallel to the given line and through point (0, -1):

Slope = 3

5


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Write the equation of a line parallel to

2x – 4y = 8 and containing (-1, 4):

– 4y = - 2x + 8

y = 1x - 2

2

Slope =1

2

y - 4 = 1(x + 1)

2


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  • Perpendicular Lines

  • **Perpendicular lines have the

  • opposite reciprocal slopes.

    • Find the slope of the original line.

    • Change the sign and invert the

    • numerator and denominator

    • of the slope.

    • Use that slope to graph your new

    • line and to write the equation

    • of your new line.


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Graph a line perpendicular to the given line and through point (1, 0):

Slope =-3

4

Perpendicular

Slope=4

3


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Write the equation of a line perpendicular to

y = -2x + 3and containing (3, 7):

Original Slope= -2

Perpendicular

Slope =1

2

y - 7 = 1(x - 3)

2


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Write the equation of a line perpendicular to

3x – 4y = 8 and containing (-1, 4):

-4y = -3x + 8

y - 4 = -4(x + 1)

3

Slope= 3

4

Perpendicular

Slope = -4

3


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