Let's go through each question step-by-step.

Question 5:

The equation provided is: $15x - 5y = -35$ We need to rearrange it into the slope-intercept form $y = mx + b$.

1. Start by isolating $y$ on one side of the equation. $-5y = -15x - 35$

2. Divide each term by $-5$ to solve for $y$. $y = 3x + 7$

So, the equation in $y = mx + b$ form is: $y = 3x + 7$ where:

• $m = 3$ (the slope)
• $b = 7$ (the y-intercept)

Question 6:

The equation given is: $y = 4000x + 50000$ where $y$ represents the total value of investments, and $x$ represents the number of years since opening the account.

Part (a):

The y-intercept ($b$) in this equation is 50,000.

Meaning: The y-intercept represents the initial amount in the account at the start (when $x = 0$), so the Zuckerbergs initially invested $50,000.

Part (b):

The slope ($m$) in this equation is 4000.

Meaning: The slope represents the annual increase in the value of the account due to additional contributions or growth. In this context, it means that each year, the account's value grows by $4,000.

Would you like further explanations on these points, or do you have additional questions?

Here are five related questions to consider:

1. How would you interpret the slope if it were negative in the context of Question 6?
2. How can you find the x-intercept of the equation in Question 5, and what does it represent?
3. How would the equation in Question 6 change if the initial investment was $60,000 instead of $50,000?
4. What would happen to the slope if the Zuckerbergs increased their annual contribution to $5,000?
5. How can the equation form $y = mx + b$ be used to predict future values?

Tip: Always isolate $y$ by dividing or moving terms systematically to achieve the slope-intercept form.