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How to Compare Linear Functions Graphs and Equations

How to Compare Linear Functions Graphs and Equations

Slope and y-intercept are used to compare the function’s graph and linear equations. This article teaches the comparison of function’s graph and linear equations.

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A step-by-step compare Linear Function’s Graph and Equations

The most common form of representation is a linear function with slope and y-intercept. In fact, the slope and y-intercept of the line as shown below are equal to m and b respectively.

f(x)=mx+b

The graph of a linear function in the coordinate plane is a straight line. To graph the line of an equation, all you have to do is find at least 2 points of the function and draw a straight line using these two points.

Slope and y-intercept are used to compare Linear Function graphs and Equations. For comparison, you should be able to get the slope and y-intercept both from the graph and from the equation.

To calculate the slope from the graph, you need to get the ratio of changes in y to the ratio of changes in x for two points located on the line. Then use the m=change in ychange in x formula. In fact, the slope is the ratio of vertical changes between two points to horizontal changes between the same two points on the line.

The y-intercept of a line is the point where the line intersects the y-axis. Find this point on the graph and compare it to the b value of the linear equation.

Comparing Linear Function’s Graph and Equations – Example 1:

Compare the slope of function A and function B

function A

function B

y=4x+1

Solution: First, find the slope m of function A. Find the change in y and the change in x points (1,0) and (0,2) on the line: m=change in ychange in x:0210=2. Now, find the slope of function B. The equation of function B in the slope-intercept form is y=4x+1. Therefore, its slope is equal to 4. In the final step, compare the slopes. The slope of function B is 4 and is greater than the slope of function A(2).

Exercises for Comparing Linear Function’s Graph and Equations

Compare the slope of function A and function B

function A

function B

y=5x+5

The slope of function B is 5 and is greater than the slope of function A(3).

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