The equation x = 0 represents a line with an undefined slope which is correct option (D).
What is slope of line?
Slope of line is defined as the angle of line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
What is undefined slope?
An undefined slope is defined as the slope of a vertical line is the undefined slope. No matter what the y coordinates are, the x coordinates remain constant. The vertical lines don't run left or right; instead, they rise or fall vertically. The slope represents the proportion of changes in the y and x coordinates.
The y-axis is parallel to any vertical line. Since a line parallel to the y-axis does not intersect it, we cannot determine its y-intercept. Therefore, no line that is perpendicular to the y-axis can be described using the intercept form.
According to equation,
Equation x = 0,
Since there is no change in x coordinates, for a vertical line, the denominator is zero which makes the slope undefined, or the slope cannot exist.
Hence, the equation x = 0 represents a line with an undefined slope.
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