Answer :
1) pages per minute is the rate. the rate is the slope pages/minutes = .4
y=.4x or y=2/5(x)
2)birdhouses per day is the slope. = .6
y=.6x or y=3/5(x)
3) miles per hour is the slope. 500/8=62.5
y=62.5x
4) square feet per minute is the slope. 40/9 =4.444444444
y=4.4444444444x or y=40/9(x)
5)miles per minutes is the rate. 5/41 is the slope.
y=5/41(x)
6) the rate is square feet per minute. 450/30=15
y=15x
y=.4x or y=2/5(x)
2)birdhouses per day is the slope. = .6
y=.6x or y=3/5(x)
3) miles per hour is the slope. 500/8=62.5
y=62.5x
4) square feet per minute is the slope. 40/9 =4.444444444
y=4.4444444444x or y=40/9(x)
5)miles per minutes is the rate. 5/41 is the slope.
y=5/41(x)
6) the rate is square feet per minute. 450/30=15
y=15x
Final answer:
The problem sets are solved by determining the rate at which each person or entity completes their task, then translating that rate into a linear equation. In all cases, the y-intercept is assumed to be 0 since no initial value is given.
Explanation:
In each of these scenarios, we need to calculate the constant rate and write it as a linear equation. Linear equations generally follow the form y = mx + b, where 'm' is the slope or rate, and 'b' is the y-intercept or initial value. However, for these problems, we can assume that the starting point or 'b' is 0 since we are not given an initial value.
- For Susan, the rate of typing is 4 pages/10 minutes or 0.4 pages per minute. The linear equation would be y = 0.4x.
- For Phil, the rate of building birdhouses is 3 birdhouses/5 days or 0.6 birdhouses per day. The linear equation would be y = 0.6x.
- For train A, the rate of traveling is 500 miles/8 hours or 62.5 miles per hour. The linear equation would be y = 62.5x.
- For Natalie, the rate of painting is 40 square feet/9 minutes or about 4.44 square feet per minute. The linear equation would be y = 4.44x.
- For Bianca, the rate of running is 5 miles/41 minutes or about 0.12 miles per minute. The linear equation would be y = 0.12x.
- For Geoff, the rate of mowing is 450 square ft/30 minutes or 15 square feet per minute. The linear equation would be y = 15x.
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