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

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

$15\ weeks$

Answer 2

It is $30 a week for 15 weeks