10.3 Slope-Intercept Form of Linear Equations

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10.3 Slope-Intercept Form of Linear Equations

• CORD Math
• Mrs. Spitz
• Fall 2006

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Objectives

• Write an equation in slope-intercept form given
  the slope and y-intercept,
• Determine the slope and y-intercepts of a graph,
  and
• Determine the x- and y-intercepts of a graph

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Assignment

• pg. 413 5-46 all

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Application

• Larry is taking home economics. As a class
  project, he is cooking dinner for some friends.
  Larry plans to spend 15 on beef and/or chicken.
  If beef costs 5 per pound and chicken costs 3
  per pound, the graph at the right shows all the
  possible combinations of beef and chicken he can
  buy. If he buys no beef, he can buy 5 pounds of
  chicken. If he buys no chicken, he can buy 3
  pounds of beef. The number 5 on the x-axis and
  the number 3 on the y-axis are called intercepts.

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More on intercepts

• The x coordinate of the point where a line
  crosses the x-axis is called the x-intercept.

• The y coordinate of the point where the line
  crosses the y-axis is called the y-intercept.

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Consider the graph below

• The line with slope m crosses the y-axis at (0,
  b). You can write an equation for this line
  using the point-slope form. Let (x1, y1 (0, b)
• y y1 m(x x1)
• y b m(x 0)
• y mx b

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Slope-Intercept Form

• Given the y-intercept b and slope m of a line,
  the slope-intercept form of an equation of the
  line is
• y mx b

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Ex. 1 State the slope and y-intercept of the
graph of y 5x 3

• y 5x 3
• y mx b

Since m 5, the slope is 5. Since b is -3, the
y-intercept is -3.
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Compare the slope-intercept form of a linear
equation with the standard form, Ax By C.
Solve for y.
If the equation is given in standard form, and B
is not zero, the slope of the line is
The y-intercept is
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Ex. 2 State the slope and y-intercept of the
graph of 3x 2y 12

• This is easy given that all the numbers are
  positive. BE CAREFUL! Negatives can really mess
  you up here.

• In the equation 3x 2y 12, A 3 B 2 and C
  12

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Ex. 2 State the slope and y-intercept of the
graph of 3x 2y 12CHECK YOUR ANSWERS!

• Write the equation in slope-intercept form.

The slope is -3/2 and the y-intercept is 6. The
solution checks.
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Recall

• Recall that the x-coordinate of the ordered pair
  for the y-intercept is 0 and the y-coordinate of
  the ordered pair for the x-intercept is 0. You
  can use these facts to find the x- and
  y-intercepts of the graph of a linear equation.

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Ex. 4 Determine the x- and y-intercepts of the
graph of 4x 5y 10

• To find the x-intercept, let y 0.
• 4x 5y 10
• 4x 5(0) 10
• 4x 10
• x 10/4
• x 5/2
• The x-intercept is 5/2. The graph crosses the
  x-axis at (5/2, 0).

• To find the y-intercept, let x 0.
• 4x 5y 10
• 4(0) 5y 10
• -5y 10
• y 10/-5
• y -2
• The y-intercept is -2. The graph crosses the
  x-axis at (0, -2).

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Formula for the x-intercept

• The y intercept of the graph of an equation in
  the form Ax By C is .
• To find the formula for the x-intercept, let y
  0
• The x intercept then is C/A, A ? 0. Therefore,
  for the graph of 2x 3y 8, the x-intercept is
  8/2 or 4, and the y-intercept is 8/3