Graph a line whose slope is 1/4 and that passes through the point (1, 0).

Steps to Solve

1. Identify the slope and point The problem states that the slope ($m$) is $\frac{1}{4}$ and the line passes through the point $(1, 0)$.

2. 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.

3. Substitute the slope into the equation Now, substitute the slope into the equation: $$y = \frac{1}{4}x + b$$

4. 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: $$b = -\frac{1}{4}$$

5. Write the final equation of the line Now, substitute $b$ back into the slope-intercept form: $$y = \frac{1}{4}x - \frac{1}{4}$$

6. 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.