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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?

Respuesta :

It is $30 a week for 15 weeks

calculista

Let

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

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

we know that

the equation that represent the situation is

[tex]y-10=-2(x-10)[/tex]

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 [tex]x=0[/tex]

substitute in the linear equation

[tex]y-10=-2(0-10)[/tex]

[tex]y-10=20[/tex]

[tex]y=\$30[/tex]

therefore

the answer part a) is

[tex]\$30[/tex]

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 [tex]y=0[/tex]

substitute in the linear equation

[tex]0-10=-2(x-10)[/tex]

[tex]0-10=-2x+20[/tex]

[tex]2x=20+10[/tex]

[tex]x=30/2=15\ weeks[/tex]

therefore

the answer part b) is

[tex]15\ weeks[/tex]

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