Question

Need help please!

14. Write an equation of a line that is parallel to the line 2x – 3y = 6. Explain how you know that the graph of
your equation is parallel to 2x – 3y = 6.

15. A student drew the line y = 2x + 3
a. Write equations for two lines that are perpendicular to this line. Justify your answer.
b. What do you notice about the slopes of these two lines? What generalization can you make about two lines
that are both perpendicular to the same line?

Answer 1

Explanation:

14. y = -2/3x + 10. This is parallel to 2x -3y because they have the same slope.

15. y = -1/2x and y = -1/2x + 2. These are perpendicular because the slope is the opposite reciprocal to the slope of y = 2x + 3, which is 2.
The slopes of the lines of the 2 equations are the same. Because of that, we can state that 2 lines that are perpendicular to the same line are parallel. This can be further supported by the Perpendicular Transversal Theorem, which says the same thing.

Hope this helps!