The problem asks to find the equation of the line in slope-intercept form $y = mx + b$ that passes through the points $(-1, -2)$ and $(0, 3)$.

Step 1: Calculate the slope ($m$)

The formula for the slope of a line passing through 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 $(-1, -2)$ and $(0, 3)$: $m = \frac{3 - (-2)}{0 - (-1)} = \frac{3 + 2}{0 + 1} = \frac{5}{1} = 5$

So, the slope of the line is $m = 5$.

Step 2: Find the y-intercept ($b$)

To find the y-intercept $b$, we use the slope-intercept form $y = mx + b$ and substitute one of the points along with the slope. Using the point $(0, 3)$: $y = mx + b \quad \Rightarrow \quad 3 = 5(0) + b \quad \Rightarrow \quad b = 3$

So, the y-intercept is $b = 3$.

Step 3: Write the equation of the line

The equation of the line is: $y = 5x + 3$

Final Answer:

The equation of the line in slope-intercept form is: $\boxed{y = 5x + 3}$

Would you like a detailed explanation of any step?

Related Questions:

1. How do you derive the slope formula for a line between two points?
2. What is the geometric meaning of the slope $m$ in a line?
3. If the points were switched, would the slope or equation change?
4. How do you verify that a given point lies on a line?
5. Can a vertical line be written in slope-intercept form?

Tip:

The slope-intercept form $y = mx + b$ is very useful for graphing because $m$ gives the steepness and $b$ is where the line crosses the y-axis.