Let's solve the problem.

We are tasked with finding the equation of a line that passes through the points $(0, -6)$ and $(-7, -12)$. The equation must be in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Calculate the slope ($m$)

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the coordinates $(0, -6)$ ($x_1 = 0, y_1 = -6$) and $(-7, -12)$ ($x_2 = -7, y_2 = -12$): $m = \frac{-12 - (-6)}{-7 - 0} = \frac{-12 + 6}{-7} = \frac{-6}{-7} = \frac{6}{7}$

So, the slope is $m = \frac{6}{7}$.

Step 2: Use the slope-intercept form to find $b$

The slope-intercept form is: $y = mx + b$ We substitute one of the points and the slope to find $b$. Using $(0, -6)$ and $m = \frac{6}{7}$: $-6 = \frac{6}{7}(0) + b$ $b = -6$

Step 3: Write the equation of the line

Now that we have $m = \frac{6}{7}$ and $b = -6$, the equation is: $y = \frac{6}{7}x - 6$

Final Answer:

The equation of the line is: $y = \frac{6}{7}x - 6$

Would you like me to explain any specific steps further?

Related Questions:

1. What is the formula to calculate the slope of a line?
2. How can you derive the slope-intercept form from a point and the slope?
3. What happens when the slope is zero? What does the graph look like?
4. How do you convert slope-intercept form into standard form?
5. Can you calculate the x-intercept of this line?

Tip:

Always use the slope formula correctly by subtracting $y_2 - y_1$ and $x_2 - x_1$ in the correct order to avoid sign mistakes.