Question

Hugo decided to pay $2 a week to his brother to buy a bicycle. The equation y – 10 = –2(x – 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay.

How much did the bicycle cost?

After how many weeks will Hugo finish paying for the bike?

Answer 1

It is $30 a week for 15 weeks

Answer 2

Let

x------> is the number of weeks

y-----> is the amount of money

we know that

the equation that represent the situation is

`y-10=-2(x-10)`

Step 1

Part a) How much did the bicycle cost?

Find the y-intercept of the linear equation

we know that

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

so

For
`x=0`

substitute in the linear equation

`y-10=-2(0-10)`

`y-10=20`

`y=\$30`

therefore

the answer part a) is

`\$30`

Step 2

Part b) After how many weeks will Hugo finish paying for the bike?

Find the x-intercept of the linear equation

we know that

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

so

For
`y=0`

substitute in the linear equation

`0-10=-2(x-10)`

`0-10=-2x+20`

`2x=20+10`

`x=30/2=15\ weeks`

therefore

the answer part b) is

`15\ weeks`