To find the equation of the line in slope-intercept form $y = mx + b$, we need to determine two key components:

1. Slope ($m$)
2. y-intercept ($b$)

Step 1: Find the Slope ($m$)

The slope is calculated using two points on the line. The two points given on the graph are:

• $(0, 7)$
• $(8, -2)$

The formula for slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Substitute the points $(0, 7)$ and $(8, -2)$:

$m = \frac{-2 - 7}{8 - 0} = \frac{-9}{8}$

So, the slope $m = -\frac{9}{8}$.

Step 2: Find the y-Intercept ($b$)

The y-intercept is the value of $y$ when $x = 0$. From the point $(0, 7)$, we can directly see that the y-intercept is $b = 7$.

Final Equation

Now, we can write the equation of the line in slope-intercept form:

$y = -\frac{9}{8}x + 7$

This is the equation of the graphed line.

Would you like any further details or explanations?

Here are 5 questions to deepen your understanding:

1. What does the slope of a line represent in geometry?
2. How would the equation change if the line passed through different points?
3. Can you calculate the slope of a vertical line?
4. What is the meaning of the y-intercept in a real-world context?
5. How would you convert this equation into standard form?

Tip: In slope-intercept form, the slope tells you how steep the line is, and the y-intercept shows where the line crosses the y-axis.