To find the equation of a line in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept, we need to follow these steps:

Step 1: Calculate the slope $m$

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Using the points $P(-3, -4)$ and $Q(-2, -2)$:

$m = \frac{-2 - (-4)}{-2 - (-3)} = \frac{-2 + 4}{-2 + 3} = \frac{2}{1} = 2$

So, the slope $m = 2$.

Step 2: Use the point-slope form of the equation

The point-slope form is: $y - y_1 = m(x - x_1)$ Using point $P(-3, -4)$ and the slope $m = 2$, we substitute into the point-slope form: $y - (-4) = 2(x - (-3))$ Simplifying: $y + 4 = 2(x + 3)$

Step 3: Simplify to slope-intercept form

Now expand and simplify the equation to get it into the form $y = mx + b$: $y + 4 = 2x + 6$ $y = 2x + 6 - 4$ $y = 2x + 2$

Final Answer:

The equation of the line in slope-intercept form is: $y = 2x + 2$

Would you like more details on any of the steps?

Here are 5 related questions for further exploration:

1. How do you find the slope when both points have the same x-coordinate?
2. Can you derive the equation if given two points with a vertical or horizontal line?
3. How can we convert from slope-intercept form to standard form?
4. What happens to the equation of a line when its slope is zero?
5. How does the slope relate to the angles a line makes with the x-axis?

Tip: To check your work, plug the coordinates of one of the given points back into the equation and verify that both sides are equal.