10.3 Slope-Intercept Form of Linear Equations

1 / 14

# 10.3 Slope-Intercept Form of Linear Equations - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about '10.3 Slope-Intercept Form of Linear Equations' - zachary

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 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
• pg. 413 #5-46 all
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
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.
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
• 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

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.

If the equation is given in standard form, and B is not zero, the slope of the line is

The y-intercept is

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

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 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.
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).

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