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All courses Math II · F-IF.7.a 21 of 73
Graph linear and quadratic functions and identify intercepts, maxima, and minima.

Use slope-intercept form to list graphing features of a line

Problem
Extract graphing features from y=2x+3.
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Hint

Read m and b separately, then express m as an integer rise over a positive run.

In y=mx+b, intercept=(0,b) and m=rise/run. Choose a positive run and carry the slope sign in the rise.

Solution walkthrough

01

Identify the form

\[y~=~2x+3\]

This is already written in slope-intercept form \(y=mx+b\).

02

Read the slope and intercept

\[\text{slope}~=~2,~y-\text{intercept}~(0,3)\]

The coefficient of \(x\) is the slope, and the constant term gives the y-intercept.

03

Use the slope to get another point

\[\text{from}~(0,3),~\text{rise}~2~\text{and}~\text{run}~1~\text{to}~\text{get}~(1,5)\]

A slope of \(2\) means up \(2\) for every \(1\) unit to the right.

04

State the graphing features

\[\text{slope}~\text{field}=m=2=2/1;~y-\text{intercept}~\text{field}=(0,3);~\text{rise}/\text{run}~\text{move}=\text{right}1,\text{up}2;~\text{second}~\text{point}=(1,5);~\text{substitution}~\text{check}=5=2·1+3\]

These are the key features needed to graph the line.

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Another way

  1. Substitute \(x=1\) into \(y=2x+3\) to get \(y=5\), which confirms the second point \((1,5)\).

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Common mistake

Using \((3,0)\) as the y-intercept because of the \(+3\), even though y-intercepts always have \(x=0\).

Answer graph labeling every exact line or quadratic feature required by the variant.
slope field=m=2=2/1; y-intercept field=(0,3); rise/run move=right1,up2; second point=(1,5); substitution check=5=2·1+3