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All courses Math I · F-IF.7.a 25 of 59
Graph linear and quadratic functions and show key features such as intercepts, maxima, and minima.

Graph a line from slope-intercept form

Problem
Graph y = 2x + 3 on the grid. State the slope and y-intercept, verify a second point, and describe the line's behavior.
Blank coordinate grid with labeled horizontal and vertical axes; no line or points are plotted.
Plot the y-intercept and use slope 2 to reach another point.
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Hint

Read \(y=2x+3\) as slope-intercept form \(y=mx+b\). The y-intercept is \(3\), so start at \((0,3)\).

In \(y=mx+b\), \(m\) is the slope and \(b\) is the y-intercept. A slope of \(2\) means rise \(2\) and run \(1\), so from \((0,3)\) you can move to \((1,5)\).

Solution walkthrough

01

Identify the slope and y-intercept

\[y~=~2x~+~3~->~m~=~2,~b~=~3\]

The equation is already in slope-intercept form \(y=mx+b\). That means the slope is 2 and the y-intercept is 3.

02

Plot the y-intercept

\[(0,3)\]

A y-intercept of 3 means the line crosses the y-axis when \(x=0\), so the intercept point is \((0,3)\).

03

Use the slope to find another point

\[\text{rise}~2,~\text{run}~1:~(0,3)~->~(1,5)\]

A slope of 2 means go up 2 units for every 1 unit to the right. Starting at \((0,3)\), that gives the point \((1,5)\).

04

Draw and describe the line

\[\text{slope}~=~2;~y-\text{intercept}~=~(0,3);~\text{second}~\text{point}~=~(1,5);~\text{checks}~=~3=2(0)+3~\text{and}~5=2(1)+3;~\text{graph}~=~\text{increasing}~\text{line}~\text{through}~\text{both}~\text{points}\]

Once the intercept and a second point are plotted, draw the straight line through them. The intercept is \((0,3)\), and another point is \((1,5)\).

+

Another way

  1. You can substitute \(x=1\) into \(y=2x+3\) to get \(y=5\), so \((1,5)\) is another point on the line.

!

Common mistake

A common mistake is to treat the \(3\) as the point \((3,0)\) instead of the y-intercept \((0,3)\). In \(y=mx+b\), the constant term gives where the line crosses the y-axis.

Coordinate graph of the line y equals 2x plus 3 with the intercept and a second point marked, annotated with slope, intercept, and a checked second point.
slope = 2; y-intercept = (0,3); second point = (1,5); checks = 3=2(0)+3 and 5=2(1)+3; graph = increasing line through both points