Question

the table below shows the temperature of the water in a lake during one week in december. water temperatures day ( x ) 1 2 3 4 5 6 7 temperature ( y ) ( 76.5^circ ) ( 75^circ ) ( 73.5^circ ) ( 72^circ ) ( 70.5^circ ) ( 69^circ ) ( 67.5^circ ) which of the following is the equation that represents this relationship? ( y = 1.5x + 75 ) ( y = -1.5x + 75 ) ( y = 1.5x + 78 ) ( y = -1.5x + 78 )

Explanation:

Step1: Determine the slope (m)

We can use two points from the table, e.g., \((x_1, y_1) = (1, 76.5)\) and \((x_2, y_2) = (2, 75)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
\(m=\frac{75 - 76.5}{2 - 1}=\frac{- 1.5}{1}=- 1.5\)

Step2: Find the y - intercept (b)

Use the slope - intercept form \(y = mx + b\) and substitute \(m=-1.5\) and a point, say \((1,76.5)\) into it.
\(76.5=-1.5\times1 + b\)
\(76.5=-1.5 + b\)
Add \(1.5\) to both sides: \(b = 76.5+1.5 = 78\)

Step3: Write the equation

The slope - intercept form of a line is \(y=mx + b\), with \(m = - 1.5\) and \(b = 78\), so the equation is \(y=-1.5x + 78\)

Answer:

\(y=-1.5x + 78\) (the option corresponding to this equation)