To find the equation of the line $y = mx + c$ that fits the data in the table, we need to determine both the slope $m$ and the y-intercept $c$.

Step 1: Find the Slope $m$

The slope $m$ for a line is calculated as: $m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$

Using two points from the table, such as $(-2, -10)$ and $(0, -4)$: $m = \frac{-4 - (-10)}{0 - (-2)} = \frac{-4 + 10}{2} = \frac{6}{2} = 3$

So, $m = 3$.

Step 2: Find the Y-Intercept $c$

To find $c$, we can use the slope-intercept form $y = mx + c$ and substitute one of the points from the table. Using $(0, -4)$: $-4 = 3 \cdot 0 + c$ $c = -4$

Conclusion

The equation of the line is: $y = 3x - 4$

Would you like further clarification or have any additional questions?

Here are some related questions to expand your understanding:

1. How would the equation change if the slope were negative?
2. How can we verify if other points lie on this line using the equation?
3. What would be the interpretation of the y-intercept in a real-world context?
4. How does the line’s equation change if we shift the line up by 2 units?
5. How can we rewrite this equation in standard form?

Tip: To find the slope quickly, use two points with simple values for easy calculation.