To find the equation of a line in slope-intercept form $y = mx + b$, we need the slope $m$ and the y-intercept $b$.

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 points $(-3, -1)$ and $(5, 5)$: $m = \frac{5 - (-1)}{5 - (-3)} = \frac{5 + 1}{5 + 3} = \frac{6}{8} = \frac{3}{4}$

Step 2: Use point-slope form to find $b$

Now that we know the slope is $m = \frac{3}{4}$, use one of the points to find the y-intercept $b$. Let's use $(5, 5)$.

Substitute the point $(5, 5)$ into the equation $y = mx + b$: $5 = \frac{3}{4}(5) + b$ Simplify: $5 = \frac{15}{4} + b$ To solve for $b$, subtract $\frac{15}{4}$ from both sides: $5 - \frac{15}{4} = b$ Convert $5$ to a fraction with denominator 4: $\frac{20}{4} - \frac{15}{4} = b$ Simplify: $b = \frac{5}{4}$

Step 3: Write the equation

Now that we know $m = \frac{3}{4}$ and $b = \frac{5}{4}$, the equation of the line is: $y = \frac{3}{4}x + \frac{5}{4}$

Would you like further details or clarifications? Here are 5 related questions to explore this topic:

1. How do you convert slope-intercept form to standard form?
2. What is the significance of the slope in real-life applications?
3. How do you find the slope if the line is vertical or horizontal?
4. Can you calculate the equation of a line parallel to the one we just found?
5. How would you find the equation of a perpendicular line?

Tip: Always double-check your slope calculation, as small sign errors can lead to incorrect answers.