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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