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



From the graph you provided, the line appears to be a straight line passing through the points \((1, 10)\) and \((4, -8)\). To find the equation of the line in slope-intercept form (\(y = mx + b\)), we need to calculate the slope \(m\) and the y-intercept \(b\).

### Step 1: Find the slope \(m\)
The slope of a line is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \((x_1, y_1) = (1, 10)\) and \((x_2, y_2) = (4, -8)\):

\[
m = \frac{-8 - 10}{4 - 1} = \frac{-18}{3} = -6
\]

### Step 2: Find the y-intercept \(b\)
Using the slope \(m = -6\) and one of the points, say \((1, 10)\), we can substitute into the slope-intercept form \(y = mx + b\) to find \(b\):

\[
10 = -6(1) + b
\]
\[
10 = -6 + b
\]
\[
b = 16
\]

### Final Equation
Now that we have \(m = -6\) and \(b = 16\), the equation of the line is:

\[
y = -6x + 16
\]

Let me know if you need further clarification or details!

### Related questions:
1. How can we calculate the slope if the points are closer on the graph?
2. What happens to the equation if the slope is positive instead of negative?
3. How do you interpret the slope of a line in terms of real-world situations?
4. How does shifting the line vertically affect the y-intercept \(b\)?
5. How would the equation change if the line were horizontal or vertical?

### Tip:
Always make sure to calculate the slope carefully by identifying two clear points on the line!

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

Learn how to find the equation of a line in slope-intercept form from a graph, using two points to calculate the slope and determine the y-intercept. This step-by-step solution includes a line passing through points (1, 10) and (4, -8) to derive the equation y = -6x + 16. Suitable for students in Grades 8-10.

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