Solve and show work please

Question

You are saving money for a new car. Your parents give you $2,000 to help your saving get started and you can save $100 weekly. Write a linear equation that determines your savings (y) for a given amount (x) of weeks saving money. Then, determine how many weeks it will take you to save for a car that costs $6,200 for a new bike. 

Answer 1

y = mx + b

y = 6200

m = 100

b = 2000

 

6200 = 100x + 2000

6200 - 2000 = 100x

4200 = 100x

4200/100 = x

x= 42

Answer 2

Hi Chantelle!

 

   We can use the slope-intercept form of a linear equation:  y = mx+b, with y and x defined as in the problem you gave.  The value "b" is the y-intercept, which we can interpret, in this case, as the amount of savings at 0 weeks.  This will be the amount of money your parents gave, as you have that money right away.  So b = 2000.

 

After that, you save 100 dollars more every week.  So your value for y (your rise) increases by 100 every time your value for x (your run) increases by 1.  So rise/run = slope = 100/1 = 100.  Slope is represented by m in the equation above.

 

So your linear equation describing this situation is:  y = 100x + 2000

 

If the car costs 6200, this is the value of y you need to have.  So you need to solve y = 100x + 2000 for the value of x when y = 6200.  In other words, solve for x when: 6200 = 100x + 2000.

 

Hope this helps!