Please help me with this, I don't understand

Question

A restaurant served 27,000 customers in 2012. In 2014, the restaurant served 28,400 customers. Write a linear model that represents the number  of customers that the restaurant serves  years after 2012. Use the model to predict the number of customers that the restaurant will serve in 2020.

Answer 1

First, make a graph and plot the points. The number of customers will be your y-axis, while the year will be your x-axis. You are given two data points and this can make two dots on your plot.

Next, connect the two dots on your plot and find the slope of this line.

Slope = (y2-y1)/(x2-x1)

Where y2 is 28,400 customers and y1 is 27,000 customers. x2 is the year 2014 and x1 is 2012.

You will find slope = 700.

Then, plug your slope into the equation y=mx+b, where m is slope.

y=700x+b

Next we find the y-intercept (b) by plugging in any x and y value given in the problem statement. For example, lets use y=27,000 customers and x=2012 the year.

27,000=700(2012) + b

Solve for b to find b=-1,381,400

Now, to find the amount of customers in 2020 we use

y=mx+b

Plug in our slope (m) of 700 and our y-intercept (b) of -1,381,400, and our x (the year 2020 as given)

y=(700)(2020) + (-1,381,400)

y = 32,600 customers as your final answer.

Hope this helps!!

Answer 2

y-y₁ = m(x-x₁)

y₁= 27000 and x₁ = 2012

y - 27000 = m(x-2012) --> y = m(x-2012) + 27000

When x = 2014, y = 28400 --> 28400 = m(2014-2012) + 27000

2m = 1400, so m = 700

y = 700(x-2012) + 27000

In 2020:

y = 700(2020-2012) + 27000 = 700(8) + 27000 = 5600 + 27000 = 326000 customers