To find the equation of the line in fully simplified slope-intercept form, $y = mx + b$, we need two key pieces of information from the graph: the slope ($m$) and the y-intercept ($b$).

Step 1: Identify two points on the line

Looking at the graph, two clear points on the line are:

• $(0, 7)$ (the y-intercept),
• $(4, -2)$.

Step 2: Calculate the slope ($m$)

The formula for the slope is:

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

Substitute the coordinates of the points $(0, 7)$ and $(4, -2)$:

$m = \frac{{-2 - 7}}{{4 - 0}} = \frac{{-9}}{{4}}$

So, the slope $m = -\frac{9}{4}$.

Step 3: Identify the y-intercept ($b$)

From the graph, the line crosses the y-axis at $y = 7$, so $b = 7$.

Step 4: Write the equation

Now that we have the slope and y-intercept, we can write the equation of the line:

$y = -\frac{9}{4}x + 7$

This is the fully simplified equation of the line in slope-intercept form.

Would you like more details or have any questions?

Here are 5 related questions to expand this topic:

1. How do you calculate the slope if you are given two points on a line?
2. What does the slope of a line tell you about its steepness and direction?
3. How can you find the equation of a line if you only know the slope and one point on the line?
4. What happens to the slope-intercept form if the line is vertical or horizontal?
5. How would the graph change if the slope were positive instead of negative?

Tip: To find the slope of any line from a graph, always pick two points that are easy to identify, such as points where the line crosses grid lines exactly.