Question

The equation 4y = 3x + 6 represents a line. What are the slopes of lines that are parallel and perpendicular to the given line? Drag the correct numbers into the boxes to complete the sentence.

Lines parallel to the given equation will have a slope of____,and lines perpendicular to the given equation will have a slope of____
a) -1/3
b) -3
c) 3/4
d) 4/3
e) -4/3
f) -3/4

Answer 1

The slope of the given line is 3/4. Lines parallel to the given line will also have a slope of 3/4, while lines perpendicular will have a slope of -4/3. Therefore the correct answer is Option E.

Step-by-step explanation:

Given the equation 4y = 3x + 6, we can determine the slope by rearranging the equation to the form y = mx + b, where m represents the slope. So, by dividing both sides of the equation by 4, we get y = (3/4)x + 3/2. Therefore, the slope of the given line is 3/4.

For lines that are parallel to the given line, they will have the same slope. So, lines parallel to 4y = 3x + 6 will also have a slope of 3/4.

On the other hand, lines that are perpendicular to the given line will have a negative reciprocal slope. The negative reciprocal of 3/4 is -4/3. Therefore, lines perpendicular to 4y = 3x + 6 will have a slope of -4/3.