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All courses Algebra I · F-IF.7.a 25 of 76
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

Decode slope-intercept form

\[y=mx+b;~y=2x+3;~m=2;~b=3\]

In y=mx+b, m is slope and b is the y-value where x=0. Thus the given equation has slope 2 and y-intercept (0,3).

02

Use the slope to locate a second point

\[m=2/1;~(0,3)~->~(1,5)\]

A slope of 2 means rise 2 for a run of 1. Starting at (0,3), move right 1 and up 2 to reach (1,5).

03

Verify both plotted points

\[3=2(0)+3;~5=2(1)+3\]

Both ordered pairs satisfy y=2x+3. On the inspected grid, which spans x=-1 to 4 and y=0 to 12, a straight line through them rises from left to right.

04

State the graph features and checks

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

The positive slope makes the line increasing, and the inspected answer SVG confirms the line and marked points within the stated coordinate bounds.

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Another way

  1. Choose x=0 and x=1, compute y=3 and y=5, then graph the unique line through those two verified points.

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Common mistake

Do not swap the coefficient and constant. In y=2x+3, 2 is the slope, while 3 is the y-coordinate of the intercept (0,3), not the point (3,0).

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

Solution walkthrough video