Question

17 multiple choice 2 points
find the slope of the line containing the points (-2,5) and (-2,0).
zero slope
-\frac{2}{3}
undefined slope
-5
18 multiple choice 2 points
the table below shows the price of rings for various weights of gemstones.
which statement best interprets the meaning of the y - intercept of the linear function that best fits these data?
the weight of the gemstone per dollar
the cost of the ring with no gemstone
the weight of the gemstone in the ring that costs $0
the price of the ring per unit of weight of the gemstone

Explanation:

Step1: Recall the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-2,5)\) and \((x_2,y_2)=(-2,0)\).

Step2: Substitute the values into the formula

Substitute the values: \(m=\frac{0 - 5}{-2-(-2)}=\frac{-5}{0}\). Division by zero is undefined.

The \(y\) - intercept of a linear function \(y = mx + b\) occurs when \(x = 0\). In the context of the problem, \(x\) represents the weight of the gemstone and \(y\) represents the price of the ring. When \(x = 0\) (no gemstone), \(y=b\). So \(b\) (the \(y\) - intercept) represents the cost of the ring with no gemstone.

Answer:

C. undefined slope