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 $A(3)$.