We are tasked with finding the equation of a line that passes through the points $(-8, -10)$ and $(0, -7)$ in slope-intercept form ($y = mx + b$). Let us calculate this step by step.

Step 1: Find the slope ($m$)

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the given points $(-8, -10)$ and $(0, -7)$: $m = \frac{-7 - (-10)}{0 - (-8)} = \frac{-7 + 10}{8} = \frac{3}{8}$

So, the slope is $m = \frac{3}{8}$.

Step 2: Use the slope-intercept form

The slope-intercept form is: $y = mx + b$ Substitute $m = \frac{3}{8}$: $y = \frac{3}{8}x + b$

Step 3: Solve for $b$ (the $y$-intercept)

Use one of the given points to solve for $b$. We use $(0, -7)$ because it's simple: $-7 = \frac{3}{8}(0) + b$ $b = -7$

Final Equation

The equation of the line is: $y = \frac{3}{8}x - 7$

Would you like further clarification or another example? Let me know!

Related Questions:

1. How do you calculate the slope of a line when given two points?
2. What is the difference between slope-intercept form and standard form?
3. How would the equation change if the slope were negative?
4. How do you graph a line given its equation in slope-intercept form?
5. Can a vertical line be expressed in slope-intercept form?

Tip:

When working with fractions, always simplify your results as much as possible to avoid errors later in calculations.