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(