To find the equation of the line in slope-intercept form, we need two things: the slope (m) and the y-intercept (b). The slope-intercept form is written as:

$y = mx + b$

Step 1: Determine the Slope

The slope $m$ is the ratio of the change in $y$ to the change in $x$ between two points on the line. Using two visible points from the graph:

• The line passes through $(0, 4)$ and $(-6, 0)$.

To calculate the slope $m$, we use the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute $(x_1, y_1) = (0, 4)$ and $(x_2, y_2) = (-6, 0)$:

$m = \frac{0 - 4}{-6 - 0} = \frac{-4}{-6} = \frac{2}{3}$

So, the slope is $\frac{2}{3}$.

Step 2: Find the y-intercept

The y-intercept $b$ is the value of $y$ when $x = 0$. From the graph, we can see that the line crosses the $y$-axis at $(0, 4)$. Therefore, $b = 4$.

Final Equation

Now that we have both the slope $m = \frac{2}{3}$ and the y-intercept $b = 4$, the equation of the line in slope-intercept form is:

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

Would you like a breakdown of how to interpret slope and intercept from graphs, or do you have any questions?

Here are some related questions:

1. How can you determine the slope from any two points on a line?
2. What is the significance of the y-intercept in a real-world context?
3. How do changes in slope affect the steepness of a line?
4. How can you rewrite the slope-intercept form in standard form?
5. What are some common mistakes when calculating slope from a graph?

Tip: Always use simple points on the line to calculate slope (points where the line clearly crosses grid lines).