use slope to solve equations

Question

Stephanie got a new job and was saving money. She has $780 in her savings account in july and $845 in august. write an equation to find how much money she would have saved in december? How much money did Stephanie start with in her savings account? Explain.

 

I am confused here because it doesn't say when she started saving. I did the problem like this:

845 - 780/1 month = $65/month   so I thought my problem is: y=65x + 845. If I solved for December I would use 4 months (August-December) y= 65*4 + 845 = $1,105.

 

But now the question of how much money did Stephanie start with in her account is throwing me...how would I know when she started saving?

Answer 1

Hi Griffin, start by finding the slope of the line represented by the information you have. If we use increments of one month on the x-axis, and increments of 65 on the y-axis, we will have two points necessary to find the slope.

 

The two points are: (7, 780) and (8, 845), since July is the 7th month and August is the 8th month, the x-values are 7 and 8. Use the dollar value for July and August for the y-values.

 

Slope = change in rise / change in run

 

Slope = (845 - 780) / (8 - 7)

 

Slope = 65 / 1

 

Knowing the slope and one point, we can use the point-slope form of the line to find the equation of the line showing Stephanie's savings.

 

Point-slope form of the line:

 

y - y₁ = m * (x - x₁)

 

Substitute for y₁, m, and x₁ using the point: (7, 780) and the slope of 65

 

y - 780 = 65 * (x - 7)

 

y - 780 = 65x - 455

 

Add 780 to both sides:

 

y = 65x + 325, this is the line that represents Stephanie's savings. 

 

To answer the question, how much did Stephanie start with in her savings account, set x = 0. The answer is $325.

 

Using the equation, we can find out how much Stephanie's account increased each month. As an example, to find out how much money Stephanie has in December, let x = 12.

 

y = 65 * 12 + 325

 

y = 1105, or Stephanie has $1105 in her savings account in December.

 

Questions?