Determine Whether Any of the Lines Given Below Are Parallel

question 110

Multiple Choice

Determine whether any of the lines given below are parallel or identical. $\begin{array} { l } L _ { 1 } : \quad x = - 8 - 4 t , y = 6 - 6 t , z = - 7 - 2 t \\L _ { 2 } : \quad x = - 4 + 4 t , y = 12 + 6 t , z = - 5 + 2 t \\L _ { 3 } : \quad x = 4 t , y = 2 - 6 t , z = 1 + 2 t \\L _ { 4 } : \quad x = - 4 - 4 t , y = 12 - 6 t , z = - 5 - 2 t\end{array}$

• A) \(L _ { 2 } , L _ { 3 }\) are identical
• B) \(L _ { 1 } , L _ { 2 } , L _ { 4 }\) are identical
• C) \(L _ { 1 } , L _ { 2 }\) are identical
• D) \(L _ { 1 } , L _ { 4 }\) are parallel
• E) \(L _ { 1 } , L _ { 3 }\) are parallel

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Definitions:

Scatterplot

A type of graph used in statistics to display values for typically two variables for a set of data.

Regression Line

A straight line that describes how a response variable y changes as an explanatory variable x changes, in linear regression analysis.

Best-Fitting Line

A line through a scatter plot of data points that best expresses the relationship between those points, often determined by the method of least squares.

Prime Time

The time period during which television audiences are the largest, often considered to be in the evening hours.