algebra

[Guest]

I have a problem i can't solve.
If someone walks 1 mile every day for a week, 1.5 miles every day for week 2, 2 miles every day for week 3, 2.5 miles every day for week 4, how do I write an equation showing this pattern?

 

[Denis]

I have a problem i can't solve.
If someone walks 1 mile every day for a week, 1.5 miles every day for week 2, 2 miles every day for week 3, 2.5 miles every day for week 4, how do I write an equation showing this pattern?

walks 1 mile in week#1, and 1/2 mile more each week, right?
let w = weeks, m = miles during w :
m = 1 + (w-1) / 2

so for week 4 (w = 4):
m = 1 + (4-1) / 2 = 1 + 3/2 = 5/2 = 2.5 : OK?

 

[soroban]

Hello, carol8!

Someone walks 1 mile every day for week 1, 1.5 miles every day for week 2,
2 miles every day for week 3, 2.5 miles every day for week 4.
How do I write an equation showing this pattern?

If you graph these pairs: \(\displaystyle (1,\,1),\2,\,1.5),\3,\,2),\4\,,2.5)\), you get a straight line.

Can you write the equation of a line through two of the points?


Using the first two points, the slope is: \(\displaystyle \,m\:=\:\frac{1.5\,-\,1}{2\,-\,1}\:=\:\frac{1}{2}\)

Using the Point-Slope Formula: \(\displaystyle \,y\,-\,1\:=\:\frac{1}{2}(x\,-\,1)\;\;\Rightarrow\;\;y\:=\;\frac{1}{2}x\,+\,\frac{1}{2}\:=\:\frac{x\,+\,1}{2}\)


We have the formula: \(\displaystyle \;\text{Miles }=\: \frac{\text{Week}\,+\,1}{2}\)