To graph the equation $4 + y = -\frac{1}{5}(x - 3)$, let's first rewrite it in slope-intercept form $y = mx + b$, which is easier to graph.

Step 1: Simplify the equation

Starting with: $4 + y = -\frac{1}{5}(x - 3)$ Subtract 4 from both sides: $y = -\frac{1}{5}(x - 3) - 4$ Now, distribute $-\frac{1}{5}$ to $(x - 3)$: $y = -\frac{1}{5}x + \frac{3}{5} - 4$ Now, convert 4 to a fraction: $y = -\frac{1}{5}x + \frac{3}{5} - \frac{20}{5}$ Combine the constant terms: $y = -\frac{1}{5}x - \frac{17}{5}$

Step 2: Identify the slope and y-intercept

The equation is now in slope-intercept form $y = mx + b$, where:

• The slope $m = -\frac{1}{5}$
• The y-intercept $b = -\frac{17}{5}$

Step 3: Graph the line

1. Plot the y-intercept: The y-intercept is $-\frac{17}{5}$, which is equivalent to $-3.4$. So, plot the point $(0, -3.4)$ on the y-axis.
2. Use the slope: The slope is $-\frac{1}{5}$, which means for every 5 units you move to the right (positive x-direction), you move 1 unit down (negative y-direction). From the point $(0, -3.4)$, move 5 units to the right and 1 unit down to get to the next point $(5, -4.4)$.
3. Draw the line: Connect the points with a straight line.

This is how you graph the line for the equation $4 + y = -\frac{1}{5}(x - 3)$.

Would you like more details, or would you like me to assist with something else?

Here are a few related questions:

1. How do you interpret the slope and y-intercept of a linear equation?
2. What are some other methods to graph a line besides slope-intercept form?
3. How do you find the equation of a line if you know two points on it?
4. What happens to the graph of the line if the slope is positive or negative?
5. How do you determine the x-intercept of a line?

Tip: To make graphing easier, always start with plotting the y-intercept and use the slope to find other points.