# 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 \(m=\frac{change \ in \ y}{change \ in \ x}\) 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 \(A(3)\).

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