A drill is used to dig down into the earth. After 2 hours, the drill is 12 meters below the surface. After 5 hours, the drill is 30 meters below the surface. Which equation represents the depth of the drill in meters, y, after ​x hours of drilling?

Answer:

6y = x

Step-by-step explanation:

All that equation is saying is that for every 1 hour drilled (x), 6 meters (y) are drilled.

y = distance in meters

x = time

12y = 2x

12y/2 = 2x/2

6y = x

30y = 5x

30y/5 = 5x/5

6y = x

The equation representing the depth of the drill in meters, y, after ​x hours of drilling is y = -6x

Since the slope is 3, hence it passes through the point (-4.67, 0). Hence the equation of the line is y = 3x + 14.

A linear equation is in the form:

y = mx + b;

where m is the slope, b is the y intercept and y, x are variables.

Let y represent the depth of drill in meters after x hours of drilling. Hence:

Since after 2 hours, the drill is 12 meters below the surface, it can be represented by (2, 12). Also after 5 hours, the drill is 30 meters below the surface, it can be represented by (5, 30)

The equation of the line is given by:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\\\y-(-12)=\frac{-30-(-2)}{5-2}(x-2) \\\\y+12=-6(x-2)\\\\y+12=-6x+12\\\\y=-6x[/tex]

The equation representing the depth of the drill in meters, y, after ​x hours of drilling is y = -6x

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Therefore the graph is attached below.

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