Graph a line whose slope is 1/4 and that passes through the point (1, 0).
Understand the Problem
The question is asking to graph a line with a specific slope (1/4) that passes through a given point (1, 0). To solve this, we will use the slope-intercept form of the equation of a line and plot it accordingly.
Answer
The equation of the line is given by: $$y = \frac{1}{4}x - \frac{1}{4}$$
Answer for screen readers
The equation of the line is given by: $$y = \frac{1}{4}x - \frac{1}{4}$$
Steps to Solve
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Identify the slope and point The problem states that the slope ($m$) is $\frac{1}{4}$ and the line passes through the point $(1, 0)$.
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Use the slope-intercept form The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
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Substitute the slope into the equation Now, substitute the slope into the equation: $$y = \frac{1}{4}x + b$$
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Find the y-intercept using the given point Substituting the point $(1, 0)$ into the equation to find $b$: $$0 = \frac{1}{4}(1) + b$$ This simplifies to: $$0 = \frac{1}{4} + b$$ Thus, solving for $b$ gives: $$b = -\frac{1}{4}$$
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Write the final equation of the line Now, substitute $b$ back into the slope-intercept form: $$y = \frac{1}{4}x - \frac{1}{4}$$
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Graph the line Using points calculated from the equation, plot the line. For example, if $x = 0$, $y = -\frac{1}{4}$. If $x = 4$, then: $$y = \frac{1}{4}(4) - \frac{1}{4} = 1 - \frac{1}{4} = \frac{3}{4}$$ Plot $(0, -\frac{1}{4})$ and $(4, \frac{3}{4})$ to draw the line.
The equation of the line is given by: $$y = \frac{1}{4}x - \frac{1}{4}$$
More Information
This line has a slope of $\frac{1}{4}$, meaning it rises 1 unit for every 4 units it runs. The y-intercept of the line is at $-\frac{1}{4}$.
Tips
- Forgetting to substitute the point correctly when solving for $b$.
- Confusing the slope with the y-intercept.
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