 Dawson Downs

2022-07-27

Create a linear relationship (equation) that you would use or rely on in your field or everyday life and explain what it is and how it is used. Identify the initial condition, such as your starting weight, and the rate of change. For a linear equation, the rate of change (slope) needs to be constant. Anaya Gregory

Expert

Step 1
I have a monthly bus pass to travel around the city. My buss pass changes a fixed a mount of $200 and a variable amount of$1.5 per mile.
Monthly cost of my travel can be obtained by wing linear equation.
If in a month i travel x miles then the total monthly cost is
$\text{Fixed change}=200\phantom{\rule{0ex}{0ex}}\text{Variable charge}=1.5×\left(x\right)=1.5x$
Step 2
Therefore total monthly cost c(x) for x miles in a month
$c\left(x\right)=1.5x+200---\left(1\right)$
If in a certain month i dont travel at all then, $x=0$
Therefore, still i have to pay $200, which is interval condition. From equation (1), we can find slope is 1.5. Hence rate of change is$1.5 per mile.

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