The Equation $$\left| \begin{array} { l l l } x & y & 1 \\x _ { 1 } & y _ { 1 } & 1 \\x _ { 2 } & y _ { 2 } & 1\end{array} \right| = 0$$

question 38

Multiple Choice

The equation $$\left| \begin{array} { l l l } x & y & 1 \\x _ { 1 } & y _ { 1 } & 1 \\x _ { 2 } & y _ { 2 } & 1\end{array} \right| = 0$$ = 0 represents an equation of the line passing through distinct points $\left( x _ { 1 } , y _ { 1 } \right)$ and $\left( x _ { 2 } , y _ { 2 } \right)$ a. Use the determinant equation to write an equation of the line passing through the given points.
b. Write the equation of the line in slope-intercept form.
- $( - 2,6 )$ and $( - 3,2 )$

• A) a. \(\left| \begin{array} { r r r } x & y & 1 \\ - 2 & 6 & 1 \\ - 3 & 2 & 1 \end{array} \right| = 0 ;\) b. \(y = - 8 x - 10\)
• B) \(\mathbf { a } . \left| \begin{array} { c c c } x & y & 1 \\ - 2 & - 3 & 1 \\ 6 & 2 & 1 \end{array} \right| = 0 ;\) b. \(y = 4 x + 14\)
• C) \(\mathbf { a } . \left| \begin{array} { c c c } x & y & 1 \\ - 2 & - 3 & 1 \\ 6 & 2 & 1 \end{array} \right| = 0 ;\) b. \(y = - 8 x - 10\)
• D) a. \(\left| \begin{array} { r r r } x & y & 1 \\ - 2 & 6 & 1 \\ - 3 & 2 & 1 \end{array} \right| = 0 ;\) b. \(y = 4 x + 14\)

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Definitions:

Cause-effect Relationships

The connection between two events where one event makes the other happen.

Correlational Research

A research method used to examine the relationship between two or more variables, without implying causation.

Experimental Research

A scientific approach that seeks to establish cause-and-effect relationships by manipulating and controlling variables.

Descriptive Research

A type of research that aims to accurately describe characteristics or phenomena, without seeking to establish cause-and-effect relationships.