Questions: Name the slope and one point that is on the line represented by the equation: x=-2 m=0 and point (-2,4) m= zero and point (5,0) m= undefined and point (-2,5) m= hidefined and point (5,-2)

Name the slope and one point that is on the line represented by the equation: x=-2
m=0 and point (-2,4)
m= zero and point (5,0)
m= undefined and point (-2,5)
m= hidefined and point (5,-2)

Transcript text: Name the slope and one point that is on the line represented by the equation: $x=-2$ $\mathrm{m}=0$ and point $(-2,4)$ $\mathrm{m}=$ zero and point $(5,0)$ $\mathrm{m}=$ undefined and point $(-2,5)$ $\mathrm{m}=$ hidefined and point $(5,-2)$

Solution

Solution Steps

The equation $ x = -2 $ represents a vertical line. The slope of a vertical line is undefined. Therefore, the correct answer is the option with an undefined slope and a point where $ x = -2 $.

Step 1: Identify the Type of Line

The equation $ x = -2 $ represents a vertical line. Vertical lines have an undefined slope because the change in $ y $ can be any value while the change in $ x $ is zero, leading to division by zero in the slope formula $ m = \frac{\Delta y}{\Delta x} $.

Step 2: Determine the Point on the Line

For a vertical line represented by $ x = -2 $, any point on the line must have an $ x $-coordinate of $-2$. Therefore, we need to find a point in the options where the $ x $-coordinate is $-2$.

Step 3: Match the Slope and Point

From the given options: