Question

Stacy needs to find the equation of line 2 such that it is perpendicular to line 1. Which of the following would NOT be enough information?

A: a graph containing both line 1 and a point on line 2
B: the slope of line 1 and a point on line 2
C: the equation of line 1 and the y intercept of line 2
D: one point on each line

Answer 1

Option D is not sufficient to find the equation of a perpendicular line, as it does not provide the slope of the original line, which is required along with a point on the new line to determine the equation.

Step-by-step explanation:

The student is asking which option would NOT provide enough information to find the equation of line 2 that is perpendicular to line 1. To determine the equation of a line that is perpendicular to another, you need the slope of the given line and a point through which the perpendicular line passes. The slope of the perpendicular line will be the negative reciprocal of the given line's slope. Considering the options:

• A: A graph containing both line 1 and a point on line 2 gives you the slope visually and a specific point to use, which is sufficient information.
• B: The slope of line 1 and a point on line 2 directly provides you with the necessary information.
• C: The equation of line 1 provides the slope, and the y-intercept of line 2 provides a point on line 2. This is also sufficient information.
• D: One point on each line does not provide the slope of line 1; thus, it is NOT enough to determine the perpendicular line's equation.

Therefore, option D would NOT be enough information to find the equation of line 2 that is perpendicular to line 1.

Answer 2

Among the options provided, the one that would NOT be enough information is C: the equation of line 1 and the y-intercept of line 2.

How to get the best option

A: A graph containing both line 1 and a point on line 2 would be enough information because it provides visual representation and a point of intersection for reference.

B: The slope of line 1 and a point on line 2 would be sufficient because knowing the slope of line 1 allows the determination of the negative reciprocal to find the perpendicular slope for line 2. Additionally, having a point on line 2 enables the equation to be determined.

C: The equation of line 1 and the y-intercept of line 2 would be enough information. Given the equation of line 1, the negative reciprocal of its slope gives the slope of line 2. Knowing the y-intercept of line 2 helps complete its equation.

D: One point on each line would be adequate information as it enables the determination of slopes and the application of the perpendicular slope relationship.