Question

Brayden is saving money to buy a new bike after 2 weeks he saved $180 after 4 weeks he saved $260 write an equation that can be used to model the number of dollars y braden saves over x weeks write your answer in slope intercept form do not include any spaces in your answer

Answer 1

The slope-intercept form is

`y=mx+b`

m is the slope

b is the y-intercept (value y at x = 0)

Since y represents the amount of money he saves and x represents the number of weeks, then

x = 2 and y = 180

x = 4 and y = 260

We will use them to find the slope

`m=(y2-y1)/(x2-x1)`

Substitute y2 by 260 and y1 by 180, x2 by 4, and x1 by 2

`\begin{gathered} m=(260-180)/(4-2) \\ m=(80)/(2) \\ m=40 \end{gathered}`

The equation is

`y=40x+b`

To find b substitute x by 2 and y by 180

`\begin{gathered} 180=40(2)+b \\ 180=80+b \end{gathered}`

Subtract 80 from both sides

`\begin{gathered} 180-80=80-80+b \\ 100=b \end{gathered}`

The equation is

`y=40x+100`