Let's work through the problem shown in the image.

The equation given is:

$10x - 5y = -15$

You are asked to rewrite this in slope-intercept form, which is:

$y = mx + b$

where $m$ is the slope, and $b$ is the y-intercept.

Step 1: Solve for $y$

Start by isolating $y$ on one side of the equation.

$10x - 5y = -15$

Subtract $10x$ from both sides:

$-5y = -10x - 15$

Step 2: Divide by $-5$ to get $y$ by itself:

$y = \frac{-10x - 15}{-5}$

Simplify the equation:

$y = 2x + 3$

Now, the equation is in slope-intercept form $y = 2x + 3$.

Step 3: Identify the slope and y-intercept

• The slope $m$ is 2.
• The y-intercept $b$ is 3.

Let me know if you need more details or have any questions. Here are 5 related questions to consider:

1. How would you solve this if the original equation had fractions?
2. Can you explain why dividing by $-5$ changes the signs of both terms?
3. How do we verify that the slope-intercept form is correct?
4. What happens to the slope and y-intercept if the equation changes to $10x + 5y = 15$?
5. How does the slope in this equation affect the graph of the line?

Tip: Remember, the slope $m$ represents how steep the line is, and the y-intercept $b$ tells you where the line crosses the y-axis.