GOZUNTA
Try it now
All courses Math I · F-IF.9 27 of 59
Compare two functions represented in different ways: equations, graphs, tables, or verbal descriptions.

Compare linear functions by slope and y-intercept

Problem
Compare the linear functions f(x)=2x+5 and g(x)=4x+1 by slope and intercept.
Your answer
Show answer choicesAnswer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
With a free account

Keep complete walkthroughs close.

Every problem included with your account keeps its hints and full solution walkthrough available for review.

Create a free account
With paid access

Learn from every walkthrough.

Unlock the complete problem bank and its worked solution walkthroughs, not only the walkthroughs in the starter set.

Compare plans

Hint

Both functions are in slope-intercept form \(y=mx+b\). Read the slope from the coefficient of \(x\) and the y-intercept from the constant term.

For \(f(x)=2x+5\), the slope is \(2\) and the y-intercept is \(5\). For \(g(x)=4x+1\), the slope is \(4\) and the y-intercept is \(1\).

Solution walkthrough

01

Read the slope of each function

\[\begin{aligned} f(x)~=~2x+5~->~\text{slope}~2 \\ g(x)~=~4x+1~->~\text{slope}~4 \end{aligned}\]

In slope-intercept form, the coefficient of \(x\) is the slope. So \(f\) has slope 2 and \(g\) has slope 4.

02

Compare the slopes

\[4~>~2\]

Since 4 is greater than 2, \(g\) has the greater slope.

03

Read the y-intercept of each function

\[\begin{aligned} f(x)~=~2x+5~->~y-\text{intercept}~5 \\ g(x)~=~4x+1~->~y-\text{intercept}~1 \end{aligned}\]

The constant term in slope-intercept form is the y-intercept. So \(f\) crosses the y-axis at 5 and \(g\) crosses at 1.

04

State the comparison

\[g~\text{has}~\text{greater}~\text{slope};~f~\text{has}~\text{greater}~y-\text{intercept}\]

Function \(g\) is steeper because its slope is larger, but function \(f\) starts higher on the y-axis because 5 is greater than 1.

+

Another way

  1. You can compare the graphs mentally: \(g(x)=4x+1\) rises faster than \(f(x)=2x+5\), but \(f\) crosses the y-axis higher.

!

Common mistake

A common mistake is to compare the whole equations instead of matching parts. Only the coefficient of \(x\) controls slope, and only the constant term controls the y-intercept.