Slope of a line is not defined if the line isa)parallel to the line x – yb)parallel to the line x+yc)parallel to Y axisd)parallel to X axisCorrect answer is option 'C'. Can you explain this answer?

Question

Slope of a line is not defined if the line isa)parallel to the line x &#8211; yb)parallel to the line x+yc)parallel to Y axisd)parallel to X axisCorrect answer is option 'C'. Can you explain this answer?

Answer

As the formula for slope is given by tan theta . where theta is angle from +ve X axis and if the line is parallel to y axis then the angle from X axis is 90 and tan 90 is not defined.

Answer

Any line parallel to y axis makes angle 90 degree with the x axis.
Hence slope = tan90 =sin90/cos90=not defined , since cos90 =0

Answer

The Slope of a Line

The slope of a line is a measure of how steep or slanted the line is. It describes the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. In other words, it represents the change in y-coordinates divided by the change in x-coordinates.

Slope of a Line: Formula

The slope of a line can be calculated using the following formula:

slope = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are any two points on the line.

Slope of a Line Parallel to the Y-Axis

When a line is parallel to the y-axis, it means that the line is vertical and does not have any horizontal change. In other words, the x-coordinate remains constant for all points on the line.

Since the formula for slope involves dividing by the change in x-coordinates, when the change in x is zero (i.e., no horizontal change), the slope is undefined. This is because division by zero is not defined in mathematics.

Why Slope is Undefined for Lines Parallel to the Y-Axis

When a line is parallel to the y-axis, it means that the x-coordinate remains constant. Let's consider two points on such a line: (x₁, y₁) and (x₂, y₂), where x₁ = x₂.

Using the slope formula, we get:

slope = (y₂ - y₁) / (x₂ - x₁)

Since x₁ = x₂, the denominator becomes zero. Division by zero is undefined in mathematics, hence the slope of a line parallel to the y-axis is undefined.

Conclusion

In conclusion, the slope of a line is not defined when the line is parallel to the y-axis. This is because division by zero is not defined in mathematics. The slope represents the ratio of the vertical change to the horizontal change, and when there is no horizontal change (i.e., the line is vertical), the slope becomes undefined.

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