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10.3 Slope-Intercept Form of Linear
EquationsCORD Math
Mrs. SpitzFall 2006
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
Assignment
•pg. 413 #5-46 all
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.
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.
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
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
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.
Compare the slope-intercept form of a linear equation with the standard form, Ax + By = C. Solve for y.
B
Cx
B
Ay
B
CAxy
B
B
CAxBy
CByAx
B
A
If the equation is given in standard form, and B is not zero, the slope of the line is
B
CThe y-intercept is
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
2
3
B
A
62
12
B
C
Ex. 2: State the slope and y-intercept of the graph of 3x + 2y = 12—CHECK YOUR ANSWERS!
• Write the equation in slope-intercept form.
2
3
B
A6
2
12
B
C
62
32
12
2
3
1232
1223
y
y
xy
yx
The slope is -3/2 and the y-intercept is 6. The solution checks.
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.
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 = 104x – 5(0) = 104x = 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 = 104(0) – 5y = 10-5y = 10 y = 10/-5 y = -2
The y-intercept is -2. The graph crosses the x-axis at (0, -2).
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
B
C
A
Cx
CAx
CBAx
CByAx
)0(
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