Want to cite, share, or modify this book? This book uses the Now we can re-label the lines as in Figure 10. Lines I and II pass through ( 0, 3 ), ( 0, 3 ), but the slope of j j is less than the slope of f f so the line for j j must be flatter. It must pass through the point (0, 3) and slant upward from left to right. ⓓ This function has a slope of 1 2 1 2 and a y-intercept of 3.This is the only function listed with a negative slope, so it must be represented by line IV because it slants downward from left to right.
![linear function graph linear function graph](http://saylordotorg.github.io/text_intermediate-algebra/section_05/d31fac765e2408cdd6a02ff500472947.png)
ⓒ This function has a slope of –2 and a y-intercept of 3.It must pass through the point ( 0, − 3 ) ( 0, − 3 ) and slant upward from left to right. ⓑ This function also has a slope of 2, but a y-intercept of − 3.Line III does not pass through ( 0, 3 ) ( 0, 3 ) so f f must be represented by Line I. Lines I and III have the same slant because they have the same slope. Function g g has the same slope, but a different y-intercept. We can use two points to find the slope, or we can compare it with the other functions listed. ⓐ This function has a slope of 2 and a y-intercept of 3.
![linear function graph linear function graph](https://mszeilstra.weebly.com/uploads/4/8/8/8/48889683/9353454_orig.png)
Choosing three points is often advisable because if all three points do not fall on the same line, we know we made an error.Īnalyze the information for each function. Evaluating the function for an input value of 2 yields an output value of 4, which is represented by the point ( 2, 4 ). Evaluating the function for an input value of 1 yields an output value of 2, which is represented by the point ( 1, 2 ). For example, given the function, f ( x ) = 2 x, f ( x ) = 2 x, we might use the input values 1 and 2. In general, we should evaluate the function at a minimum of two inputs in order to find at least two points on the graph. We then plot the coordinate pairs on a grid.
![linear function graph linear function graph](https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/revati-f-linear-graph-02-1605708624.png)
The input values and corresponding output values form coordinate pairs. To find points of a function, we can choose input values, evaluate the function at these input values, and calculate output values. And the third is by using transformations of the identity function f ( x ) = x. The second is by using the y-intercept and slope. The first is by plotting points and then drawing a line through the points. There are three basic methods of graphing linear functions. By graphing two functions, then, we can more easily compare their characteristics. We were also able to see the points of the function as well as the initial value from a graph. In Linear Functions, we saw that that the graph of a linear function is a straight line. In this section, we will consider methods of comparing functions using graphs. To solve the problem, we will need to compare the functions. The total cost of each payment plan can be represented by a linear function. A consumer wants to determine whether the two plans will ever cost the same amount for a given number of long distance minutes used. The two plans charge the same rate per long distance minute, but charge a different monthly flat fee. Two competing telephone companies offer different payment plans.