Question

I need the answer to the three questions I am struggling very hard to do this so I need help with the three questions

Answer 1

Answer:

Part 1) The slope is $m=25$ (the cost of the gym is $25 per month)

Part 2) The y-intercept is the point (0,-100) see the explanation

Part 3) $y=25x-100$, After 14 months the cost is $\ 250$

Step-by-step explanation:

Part 1) What is the slope of the line

Let

x ---> the number of months

y ---> the total cost in dollars

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

From the graph take two points

(0,-100) and (4,0)

substitute the values in the formula

$m=\frac{0+100}{4-0}$

$m=\frac{100}{4}$

$m=25$

Remember that the slope is equal to the unit rate of the linear equation

That means ----> the cost of the gym is $25 per month

Part 2) What is the y-intercept of the line

we know that

The y-intercept is the value of y when the value of x is equal to zero

Looking at the graph the y-intercept is the point (0,-100)

In context this problem, the y-intercept represent the rebate of $100 that the gym was offering for sign up for a full year      

Part 3) What is the linear equation for the line in this situation? What is the cost of the gym membership after 14 months

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept      

we have

$m=25$

$b=-100$

substitute the values

$y=25x-100$

For x=14 months

substitute

$y=25(14)-100$

$y=350-100=\ 250$