To graph the equation:

$y + 5 = \frac{1}{4}(x - 1)$

Step 1: Rearrange the equation into slope-intercept form $y = mx + b$.

Start by isolating $y$:

$y = \frac{1}{4}(x - 1) - 5$

Simplify the equation:

$y = \frac{1}{4}x - \frac{1}{4} - 5$

$y = \frac{1}{4}x - \frac{1}{4} - \frac{20}{4}$

$y = \frac{1}{4}x - \frac{21}{4}$

Now we have the equation:

$y = \frac{1}{4}x - \frac{21}{4}$

This is in slope-intercept form where:

• Slope (m) = 1/4
• y-intercept (b) = -21/4 or -5.25

Graphing Steps:

1. Start at the y-intercept $(-21/4 \text{ or } -5.25)$, which is just below $-5$ on the y-axis.
2. From this point, use the slope $\frac{1}{4}$, which means for every 4 units you move horizontally to the right (positive x-direction), move 1 unit up.

Would you like me to graph this for you or go over the steps in more detail?

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Here are some related questions you might find useful:

1. How do you interpret the slope and y-intercept of a line?
2. What happens if the slope is negative instead of positive?
3. How can you graph a line using two points instead of slope-intercept form?
4. What is the general form of a linear equation?
5. How can you write the equation of a line given two points?

Tip: When graphing, it's often useful to start with the y-intercept and then use the slope to find other points.