A water tank is being drained at a constant rate. After 3 hours of draining, the tank cont… — ACT

A water tank is being drained at a constant rate. After $3$ hours of draining, the tank contains $120$ gallons of water. After $5$ hours of draining, the tank contains $80$ gallons of water. If the volume of water in the tank, $y$ (in gallons), is modeled as a linear function of the time spent draining, $x$ (in hours), what is the slope of the line representing this function in the standard $(x, y)$ coordinate plane?

A
$20$
B
$-\frac{1}{20}$
$-20$ Cevap
D
$-11$
E
$53$

Cevap

-20

The correct answer is

-20

. The slope

m

of a line passing through two points

(x_1, y_1)

and

(x_2, y_2)

is given by the formula

m = \frac{y_2 - y_1}{x_2 - x_1}

. Identifying the points from the problem as

(3, 120)

and

(5, 80)

, we calculate the slope as

m = \frac{80 - 120}{5 - 3} = \frac{-40}{2} = -20

. This represents a constant rate of change of

-20

gallons per hour.

Adım Adım Çözüm

Identify the coordinates of the two data points from the problem statement.

The two points on the line are

(3, 120)

and

(5, 80)

, where

x

represents the time in hours and

y

represents the volume of water in gallons.

To calculate the slope of a line, we first need to identify the coordinate points

(x_1, y_1)

and

(x_2, y_2)

that lie on the line.

Substitute the coordinates into the slope formula,

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{80 - 120}{5 - 3}

The slope represents the constant rate of change, which is the change in the dependent variable (

y

) divided by the change in the independent variable (

x

Simplify the expression to find the final value of the slope.

m = \frac{-40}{2} = -20

Performing the subtraction and division gives the slope of the line, showing that the volume of water decreases by

20

gallons per hour.

Anahtar Kavram

The slope of a line, representing a constant rate of change, is calculated using the formula

m = \frac{y_2 - y_1}{x_2 - x_1}

for any two points

(x_1, y_1)

and

(x_2, y_2)

on the line.

Tahmini Süre:1m 0s

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Cevap

Adım Adım Çözüm

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