To solve the equation of the line, we need to find the slope $m$ and the y-intercept $c$ in the line equation form $y = mx + c$.

Step 1: Determine the slope $m$

The slope of a line is calculated as: $m = \frac{\Delta y}{\Delta x}$ This means the change in $y$ over the change in $x$ between two points on the line.

From the graph:

• One point on the line is $(-9, 40)$
• Another point is $(6, -10)$

Now, calculate the slope: $m = \frac{-10 - 40}{6 - (-9)} = \frac{-50}{6 + 9} = \frac{-50}{15} = \frac{-10}{3}$

Step 2: Find the y-intercept $c$

The y-intercept is the point where the line crosses the y-axis. From the graph, this happens when $x = 0$. Visually, it appears that the line crosses the y-axis at approximately $y = 20$.

So, $c = 20$.

Final Equation

Substitute $m = -\frac{10}{3}$ and $c = 20$ into the equation: $y = -\frac{10}{3}x + 20$

This is the equation of the line.

Would you like more details on any step, or do you have any questions?

Here are 5 related questions:

1. What does the slope of a line represent geometrically?
2. How do you find the equation of a line using two points?
3. What are some ways to confirm if a point lies on a line?
4. What is the significance of the y-intercept in real-world problems?
5. How can graphing software assist in verifying equations?

Tip: Remember, the slope of a line indicates the steepness, and its sign tells whether the line is increasing or decreasing.