1Cademy - Graphing $$y = \frac{1}{2}x + 3$$ by Plotting Points

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Choosing Strategic $x$ -Values for Fraction Coefficients

Example

Graphing $y = \frac{1}{2}x + 3$ by Plotting Points

To graph $y = \frac{1}{2}x + 3$ , apply the Point-Plotting Method while choosing $x$ -values strategically to avoid fractional results.

Step 1 — Find three solution points. Because the coefficient of $x$ is $\frac{1}{2}$ , select $x$ -values that are multiples of $2$ so that the product $\frac{1}{2} \cdot x$ is a whole number:

$x = 0$ : $y = \frac{1}{2}(0) + 3 = 0 + 3 = 3$ , giving $(0, 3)$
$x = 2$ : $y = \frac{1}{2}(2) + 3 = 1 + 3 = 4$ , giving $(2, 4)$
$x = 4$ : $y = \frac{1}{2}(4) + 3 = 2 + 3 = 5$ , giving $(4, 5)$

Step 2 — Plot the points. Mark $(0, 3)$ , $(2, 4)$ , and $(4, 5)$ on a rectangular coordinate system. All three points line up, confirming the calculations are correct.

Step 3 — Draw the line. Connect the three points with a straight line, extend it across the grid, and add arrows on both ends. The resulting line is the graph of $y = \frac{1}{2}x + 3$ .

Updated 2026-04-21

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