Question

solve for x
11.
solve for x
13.
14.

1. true or false the slopes of perpendicular lines have a product of - 1.

true false

1. find the slope of a line that is perpendicular to the equation 2y+3x = 4

a. 3/2 b. - 3/2 c. - 2/3 d. 2/3 e. 3/1

1. find the equation of the line that is parallel to 4y+5x = 8 and passes through the point (- 1,2)
2. find the equation of a line that is perpendicular to 5y - 3x = 4 and passes through the point (3, - 1)

Explanation:

Step1: Solve for x in problem 13

Set the two - angle expressions equal as they are vertical angles. So, \(5x + 13=6x + 3\).
Subtract \(5x\) from both sides: \(13=x + 3\).
Subtract 3 from both sides: \(x = 10\).

Step2: Answer problem 16

The slopes of perpendicular lines have a product of - 1. So the statement "the slopes of perpendicular lines have a product of 1" is False.

Step3: Answer problem 17

First, rewrite the line \(2y+3x = 4\) in slope - intercept form \(y=mx + b\) where \(m\) is the slope.
Solve for \(y\): \(2y=-3x + 4\), then \(y=-\frac{3}{2}x+2\), the slope of this line is \(-\frac{3}{2}\).
The slope of a line perpendicular to it is the negative reciprocal, which is \(\frac{2}{3}\).

Answer:

1. \(x = 10\)
2. False
3. \(\frac{2}{3}\)