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the value of a car decreases at a constant rate. after 3 years the value of the car is 15,000. after 2 more years, the value of the car is 11,000 write and solve a linear equation to find what Fahrenheit temperature this is.

Respuesta :

Answer:

The linear equation is : y = -2000·x + 21000

Step-by-step explanation:

Let the time be denoted by x and the value of the car be denoted by y

After 3 years the value is 15000

[tex]\implies x_1 = 3\text{ and }y_1 = 15000[/tex]

So, point is (3,15000)

After 2 years the value is 11000

[tex]\implies x_2 = 2 + 3 = 5\text{ and }y_2 = 11000[/tex]

So, point is (5,11000)

Now, to find the linear equation we need to find the slope(m) of these two obtained points : (3,15000) and (5,11000)

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{11000-15000}{5-3}\\\\m=-2000[/tex]

So, the required linear equation will be :

[tex]y-y_1=m\cdot (x-x_1)[/tex]

y  -15000 = -2000·(x - 3)

⇒ y - 15000 = -2000·x + 6000

⇒ y = -2000·x + 21000

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