Answer :
Sure! Let's solve each part of the problem step by step.
### Part a: Ted and Hot Wheels Cars
1. Identify the initial amount and rate of change:
- Ted currently owns 10 hot wheels cars. This is your starting point, or y-intercept (b).
- He plans to buy 20 new cars every year. This is the rate of change, or slope (m).
2. Write the equation:
- The equation of a line in the slope-intercept form is [tex]\( y = mx + b \)[/tex].
- For Ted's scenario, it becomes [tex]\( y = 20x + 10 \)[/tex].
3. Determine the number of hot wheels in 13 years:
- Substitute x with 13 in the equation:
[tex]\[
y = 20(13) + 10
\][/tex]
- Calculate:
[tex]\[
y = 260 + 10 = 270
\][/tex]
So, Ted will have 270 hot wheels cars in 13 years.
### Part b: Todd and Garden Weeds
1. Identify the initial situation and rate of change:
- Todd initially has 1,000 square feet of garden weeds. This is the starting point, or y-intercept (b).
- He removes 15 square feet of weeds every minute. Since the weeds are being taken away, this is a negative rate of change, or slope (-m).
2. Write the equation:
- The equation here reflects a decrease in weeds, [tex]\( y = -15x + 1000 \)[/tex].
3. Determine how many square feet of yard will still be left after 30 minutes:
- Substitute x with 30 in the equation:
[tex]\[
y = -15(30) + 1000
\][/tex]
- Calculate:
[tex]\[
y = -450 + 1000 = 550
\][/tex]
Therefore, 550 square feet of the garden will still have weeds after 30 minutes.
I hope this helps you understand the solution! Let me know if you have any questions.
### Part a: Ted and Hot Wheels Cars
1. Identify the initial amount and rate of change:
- Ted currently owns 10 hot wheels cars. This is your starting point, or y-intercept (b).
- He plans to buy 20 new cars every year. This is the rate of change, or slope (m).
2. Write the equation:
- The equation of a line in the slope-intercept form is [tex]\( y = mx + b \)[/tex].
- For Ted's scenario, it becomes [tex]\( y = 20x + 10 \)[/tex].
3. Determine the number of hot wheels in 13 years:
- Substitute x with 13 in the equation:
[tex]\[
y = 20(13) + 10
\][/tex]
- Calculate:
[tex]\[
y = 260 + 10 = 270
\][/tex]
So, Ted will have 270 hot wheels cars in 13 years.
### Part b: Todd and Garden Weeds
1. Identify the initial situation and rate of change:
- Todd initially has 1,000 square feet of garden weeds. This is the starting point, or y-intercept (b).
- He removes 15 square feet of weeds every minute. Since the weeds are being taken away, this is a negative rate of change, or slope (-m).
2. Write the equation:
- The equation here reflects a decrease in weeds, [tex]\( y = -15x + 1000 \)[/tex].
3. Determine how many square feet of yard will still be left after 30 minutes:
- Substitute x with 30 in the equation:
[tex]\[
y = -15(30) + 1000
\][/tex]
- Calculate:
[tex]\[
y = -450 + 1000 = 550
\][/tex]
Therefore, 550 square feet of the garden will still have weeds after 30 minutes.
I hope this helps you understand the solution! Let me know if you have any questions.
