To graph the equation $y - 7 = \frac{1}{4}(x + 5)$, we can follow these steps:

Step 1: Rewrite the equation in slope-intercept form ($y = mx + b$)

Start by simplifying the equation:

$y - 7 = \frac{1}{4}(x + 5)$

First, distribute $\frac{1}{4}$ to $(x + 5)$:

$y - 7 = \frac{1}{4}x + \frac{5}{4}$

Now, isolate $y$ by adding 7 to both sides:

$y = \frac{1}{4}x + \frac{5}{4} + 7$

To combine $\frac{5}{4} + 7$, express 7 as $\frac{28}{4}$:

$y = \frac{1}{4}x + \frac{5}{4} + \frac{28}{4} = \frac{1}{4}x + \frac{33}{4}$

Now, the equation is in slope-intercept form:

$y = \frac{1}{4}x + \frac{33}{4}$

Step 2: Identify the slope and y-intercept

• Slope $m = \frac{1}{4}$
• y-intercept $b = \frac{33}{4}$ or 8.25

Step 3: Plot the graph

1. Start by plotting the y-intercept $(0, 8.25)$ on the y-axis.
2. Using the slope $\frac{1}{4}$, for every 4 units you move horizontally (right), move 1 unit vertically (up).

From the y-intercept $(0, 8.25)$, plot another point at $(4, 8.25 + 1) = (4, 9.25)$. Continue this process to extend the line.

Graph Summary:

• The line will have a positive slope of $\frac{1}{4}$, meaning it rises slowly as you move to the right.
• The y-intercept is $(0, 8.25)$, so the line starts slightly above 8 on the y-axis.

Would you like more details on how to plot this or another step-by-step breakdown?

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Related Questions:

1. How do you determine the slope and y-intercept from an equation in standard form?
2. How do you graph a line with a negative slope?
3. What is the significance of the slope in real-world situations?
4. How do you find the equation of a line given two points?
5. What is the difference between slope-intercept form and point-slope form?

Tip:

When graphing lines with fractions in the slope, it can help to multiply through by the denominator to avoid dealing with fractions while plotting.