It seems the image you uploaded contains some equations and mathematical work related to solving a line equation using the point-slope formula. Let's break this down step by step.

From the image, the equation you seem to be working with is the point-slope formula:

$y - y_1 = m(x - x_1)$

Where:

• $m$ is the slope (gradient),
• $(x_1, y_1)$ is a point on the line.

The equation appears to be used in two different scenarios:

1. The first case mentions a line with slope $m = 0$, which corresponds to a horizontal line. You substituted into the formula $y - (-3) = 0(x - (-2))$, simplifying to $y + 3 = 0$. This is the equation of a horizontal line passing through $(-2, -3)$.

2. The second case involves a line passing through the point $(3, 5)$ with a slope of 1. You correctly used the point-slope formula to get:

$y - 5 = 1(x - 3)$

Which simplifies to:

$y - 5 = x - 3$

And further simplifies to:

$y = x + 2$

3. The third case seems to discuss a line passing through the origin, where the slope is infinite ($m = \infty$), corresponding to a vertical line.

Let me know if you'd like more detailed steps for any of these equations, or if you need help with another problem!

Here are a few related questions that might help expand your understanding:

1. How do you calculate the slope of a line given two points?
2. What is the general form of the equation of a vertical line?
3. How do you convert a point-slope form equation to slope-intercept form?
4. What is the significance of an infinite slope in the context of line equations?
5. How do you determine whether two lines are parallel or perpendicular from their equations?

Tip: Always check if the slope is zero (horizontal) or infinite (vertical) to simplify your work with those specific lines!