To find the equation of the line in slope-intercept form $y = mx + b$, we first need to calculate the slope $m$ and then use it to find the y-intercept $b$.

Step 1: Find the slope (m)

The slope $m$ is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(-7, 0)$ and $(7, -2)$: $m = \frac{-2 - 0}{7 - (-7)} = \frac{-2}{7 + 7} = \frac{-2}{14} = -\frac{1}{7}$ So, the slope $m = -\frac{1}{7}$.

Step 2: Find the y-intercept (b)

Now that we have the slope, we can use one of the points (I'll use $(-7, 0)$) to find the y-intercept $b$. Plugging into the equation $y = mx + b$: $0 = -\frac{1}{7}(-7) + b$ Simplifying: $0 = 1 + b \quad \Rightarrow \quad b = -1$

Step 3: Write the equation of the line

Now that we know the slope $m = -\frac{1}{7}$ and the y-intercept $b = -1$, the equation of the line in slope-intercept form is: $y = -\frac{1}{7}x - 1$

Would you like more details or have any questions?

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Here are 5 related questions you might find useful:

1. How do you find the equation of a line given two points?
2. What is the relationship between the slope and the angle of a line?
3. How do you convert the equation of a line from slope-intercept form to standard form?
4. How does changing the slope affect the steepness of a line?
5. What is the significance of the y-intercept in real-world problems?

Tip: Always double-check your slope calculation, especially the signs, as they can change the direction of the line.