10 3 slope intercept form of linear equations l.
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10.3 Slope-Intercept Form of Linear Equations. CORD Math Mrs. Spitz Fall 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.

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objectives
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
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.Application
more on intercepts
The x coordinate of the point where a line crosses the x-axis is called the x-intercept.More on intercepts
  • 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

Consider the graph below
slope intercept form
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
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
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

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

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

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

recall
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 = 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).

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

Formula for the x-intercept