Answer:
The answer is below
Step-by-step explanation:
A) i)
For Anna initially, she has $0 from making 0 envelopes. After making 400 envelopes she has $20. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:
![y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{20-0}{400-0}(x-0)\\\\y=\frac{1}{20} x](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%28x-x_1%29%5C%5C%5C%5Cy-0%3D%5Cfrac%7B20-0%7D%7B400-0%7D%28x-0%29%5C%5C%5C%5Cy%3D%5Cfrac%7B1%7D%7B20%7D%20x)
The table is:
x: 200 400 600 800 1000
y: 10 20 30 40 50
ii)
For Jason initially, he has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:
![y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{10-0}{250-0}(x-0)\\\\y=\frac{1}{25} x](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%28x-x_1%29%5C%5C%5C%5Cy-0%3D%5Cfrac%7B10-0%7D%7B250-0%7D%28x-0%29%5C%5C%5C%5Cy%3D%5Cfrac%7B1%7D%7B25%7D%20x)
The table is:
x: 200 400 600 800 1000
y: 8 16 24 32 40
The graph is plotted using geogebra online graphing
b) From the table above we can see that Anna makes more stuffing than Jason.
c) Anna has a savings of $100. Hence this can be represented by the points (0, 100) and (250, 10). Using the equation of a line:
![y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-100=\frac{20-0}{400-100}(x-0)\\\\y=\frac{1}{15} x+100](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%28x-x_1%29%5C%5C%5C%5Cy-100%3D%5Cfrac%7B20-0%7D%7B400-100%7D%28x-0%29%5C%5C%5C%5Cy%3D%5Cfrac%7B1%7D%7B15%7D%20x%2B100)
We can see from the graph that there is a y intercept at 100. That is the earnings starts from 100.
The equation of a line is given as y = mx + b, where m is the slope and b is the y intercept (initial value)
For the first graph, the slope is 1/20 and the initial value is 0 while for the second graph the slope is 1/15 and the initial value is 100
D) The line pass through (10, 10) and (100, 40), hence:
![y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{40-10}{100-10}(x-10)\\\\y-10=\frac{1}{3} (x-10)\\\\y=\frac{1}{3}x+\frac{20}{3}](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%28x-x_1%29%5C%5C%5C%5Cy-10%3D%5Cfrac%7B40-10%7D%7B100-10%7D%28x-10%29%5C%5C%5C%5Cy-10%3D%5Cfrac%7B1%7D%7B3%7D%20%28x-10%29%5C%5C%5C%5Cy%3D%5Cfrac%7B1%7D%7B3%7Dx%2B%5Cfrac%7B20%7D%7B3%7D)