Question

if you are given the graph of a line and are asked to write the equation of a perpendicular line, does it matter what the y - intercept will be for the equation you write? why or why not?

what the y - intercept of the new line is. the new equations slope

the new equations y - intercept

Explanation:

Two lines are perpendicular if their slopes are negative reciprocals, regardless of their y-intercepts. A line with any y-intercept will be perpendicular to the original line as long as its slope follows the perpendicular slope rule. However, if the problem requires the perpendicular line to pass through a specific point, the y-intercept is fixed; otherwise, it can be any value.

Answer:

It does not matter what the y-intercept is (unless the problem specifies the perpendicular line must pass through a particular point).

• The new equation's slope must be the negative reciprocal of the original line's slope to ensure perpendicularity.
• The new equation's y-intercept can be any real number because changing the y-intercept only shifts the line vertically, which does not affect the perpendicular relationship between the two lines.