1Cademy - Graphing $$y = 0.2x + 45$$ Using its Slope and y-Intercept

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Graphing a Line Using its Slope and y-Intercept

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Graphing $y = 0.2x + 45$ Using its Slope and y-Intercept

To graph $y = 0.2x + 45$ , use a coordinate grid with axes extended from about $-80$ to $80$ , since the y-intercept at $45$ does not fit on a standard $-10$ to $10$ grid.

Step 1 — Find the slope-intercept form. The equation $y = 0.2x + 45$ is already in the form $y = mx + b$ .

Step 2 — Identify the slope and y-intercept. The slope is $m = 0.2$ and the y-intercept is $(0, 45)$ .

Step 3 — Plot the y-intercept. Mark the point $(0, 45)$ on the coordinate plane.

Step 4 — Count out the rise and run. The slope $m = 0.2$ can be written as the fraction $\frac{2}{10}$ . However, given the large scale of the graph, using the equivalent fraction $\frac{10}{50}$ produces step sizes that are easier to work with on the extended grid. The rise is $10$ and the run is $50$ .

Step 5 — Mark the second point. Starting at $(0, 45)$ , move up $10$ units and right $50$ units to reach $(50, 55)$ .

Step 6 — Connect the points with a line. Draw a straight line through $(0, 45)$ and $(50, 55)$ .

This example demonstrates two practical techniques: converting a decimal slope to a fraction ( $0.2 = \frac{2}{10}$ ), and then replacing that fraction with an equivalent one ( $\frac{10}{50}$ ) whose rise and run better fit the graph's extended scale.

Updated 2026-04-21

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OpenStax Elementary Algebra

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