# 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.

## 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 $$m=\frac{change \ in \ y}{change \ in \ x}$$ 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: $$m=\frac{change \ in \ y}{change \ in \ x}: \frac{0-2}{-1-0}=2$$. 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 $$A(3)$$.

### What people say about "How to Compare Linear Functions Graphs and Equations - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.

X
30% OFF

Limited time only!

Save Over 30%

SAVE $5 It was$16.99 now it is \$11.99