1 / 12

Understanding Linear Functions and Graphs

Learn about linear functions, slopes, y-intercepts, graphs of equations, and the vertical line test. Explore examples and practical applications.

rrowlands
Download Presentation

Understanding Linear Functions and Graphs

An Image/Link below is provided (as is) to download presentation 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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 1.2 Linear Functions and Graphs

  2. EXAMPLE The following table shows the cost per day for a rental car depending on how many miles you drive a day.

  3. LINEAR FUNCTIONS Definition: A linear function is a function of the form f (x) = mx + b. NOTE: The letters “m” and “b” represent coefficients (numbers).

  4. STRAIGHT LINES ANDLINEAR GRAPHS The graph of the linear function f (x) = mx + b is the straight line consisting of all the points (x,y) in the xy-plane that satisfy the equation y = mx + b.

  5. SLOPE AND y-INTERCEPTOFA LINE • The y-value where a line crosses the y-axis is called the y-intercept. • The slope of a line in the xy-plane is defined by

  6. SLOPE-INTERCEPTEQUATION • The constant b is the y-intercept of the line. • The coefficient m of x is the slope of the line. • This equation is called the slope-intercept equation for a line. In the equation y = mx + b,

  7. If (x0, y0) is a fixed point on a line, and (x, y) is any other point on the line, we can find the slope by The equation is called the point-slope equation for the line with slope m that passes through the point (x0, y0). POINT-SLOPE FORMULAFOR A LINE

  8. GRAPHS OF EQUATIONS Definition: The graph of an equation involving two variables x and y consists of all points in the xy-plane whose coordinates (x, y) satisfy the equation.

  9. GRAPHS OF LINES There are three types of equations whose graphs are straight lines: • Equations whose graphs are vertical lines. These have the form x = constant. • Equations whose graphs are horizontal lines. These have the form y = constant. • Equations whose graphs are slanted lines (lines that are neither vertical or horizontal). These have the form y = mx + b.

  10. GRAPH OF A FUNCTION Definition: The graph of the function f is the graph of the equation y = f (x).

  11. THE VERTICAL LINE TEST Recall that a function assigns to each number x a specific number f (x). Thus, a graph is the graph of a function if and only if no vertical line intersects the graph at more than one point.

  12. EXAMPLE The following table shows the cost per day for a rental car depending on how many miles you drive a day. • How many miles did you drive if the cost was $80? • What do the slope and y-intercept mean in practical terms?

More Related