Question

A company has a manufacturing plant that is producing quality canisters. They find that in order to produce 300 canisters in a month, it will cost $7400. Also, to produce 310 canisters in a month, it will cost $7550. Find an equation in the form y = mx + b, where r is the number of canisters produced in a month and y is the monthly cost to do so.
Answer: y =______

Answer 1

Answer:

$y = 15x + 2900$

Step-by-step explanation:

Given:

A company has find that in order to produce 300 canisters in a month, it will cost $7400. Also, to produce 310 canisters in a month, it will cost $7550.

Let $x_{1}=300$, $y_{1}=7400$, $x_{2}=310$, and $y_{2}=7550$

Find an equation in the form $y = mx + b$------(1)

where x is the number of canisters produced in a month and y is the monthly cost to do

we know slope of line m = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Put all required value in above equation.

m = $\frac{7550-7400}{310-300}$

m = $\frac{150}{10}$

$m=15$

Put m value in equation 1.

$y = 15x + b$

For b we put $y=7400$ and $x=300$ in above equation.

$7400 = 15\times 300 + b$

$7400 = 4500 + b$

$7400 - 4500 = b$

$b=2900$

Put m and b value in equation 1.

$y = 15x + 2900$

Therefore, the equation is $y = 15x + 2900$