The given equation is:

$y + 3 = -\frac{2}{3}(x - 4)$

To graph the line, we can rewrite it in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Simplify the equation

Distribute the $-\frac{2}{3}$ to the $(x - 4)$:

$y + 3 = -\frac{2}{3}x + \frac{8}{3}$

Step 2: Isolate $y$

Subtract 3 from both sides:

$y = -\frac{2}{3}x + \frac{8}{3} - 3$

Convert 3 to have a denominator of 3:

$y = -\frac{2}{3}x + \frac{8}{3} - \frac{9}{3}$

Now simplify:

$y = -\frac{2}{3}x - \frac{1}{3}$

Final Equation:

$y = -\frac{2}{3}x - \frac{1}{3}$

Graphing the Line:

• The slope $m = -\frac{2}{3}$ means the line goes down 2 units for every 3 units to the right.
• The y-intercept is $-\frac{1}{3}$, so the line crosses the y-axis at $-\frac{1}{3}$.

Would you like further details on plotting or any other explanation?

Related Questions:

1. What does the slope tell us about the steepness of the line?
2. How do you convert any linear equation into slope-intercept form?
3. How do you interpret the y-intercept in a real-world scenario?
4. What happens to the graph if the slope is positive?
5. Can you graph this line using points instead of the slope?

Tip: When graphing lines, always start by plotting the y-intercept, then use the slope to determine the next points on the line.