Understanding Slopes and Line Characteristics

The video tutorial explains how to find the slope of a line given two points and determine if the line is increasing, decreasing, horizontal, or vertical. It covers the calculation of slope by finding the change in y divided by the change in x, and explains the implications of positive, negative, zero, and undefined slopes. Two examples are provided to demonstrate the calculation process, and the results are visualized on a coordinate plane to confirm the line's characteristics.

What is the first step in finding the slope of a line given two points?

• Subtract the x-coordinates from the y-coordinates

• Add the x-coordinates together

• Calculate the change in y and divide by the change in x

• Find the midpoint of the points

If a line has a positive slope, what does this indicate about the line?

• The line is horizontal

• The line is vertical

• The line is increasing

• The line is decreasing

What does a slope of zero indicate about a line?

• The line is horizontal

• The line is decreasing

• The line is increasing

• The line is vertical

In the first example, what is the calculated slope of the line?

• +1/12

• -1/15

• +1/15

• -1/12

What is the least common denominator used for the y-coordinates in the first example?

• 6

• 8

• 10

• 12

In the second example, what is the slope of the line?

• -19/12

• -1/15

• -95/64

• -5/4

What is the least common denominator used for the x-coordinates in the second example?

• 12

• 15

• 10

• 20

What does a negative slope indicate about the direction of a line?

• The line is vertical

• The line is increasing

• The line is horizontal

• The line is decreasing

What is the purpose of plotting the points on a coordinate plane in the conclusion?

• To confirm the calculated slopes and their implications

• To check if the lines are parallel

• To determine the length of the lines

• To find the midpoint of the lines

What happens to the y-values as x increases in a line with a positive slope?

• Y-values decrease

• Y-values remain constant

• Y-values increase

• Y-values become undefined