Understanding the Y-Intercept and Slope of a Line

The video tutorial explains how to determine the Y-intercept of a line on a graph. It begins by introducing the concept of the Y-intercept and the equation of a line, Y = mx + b, where m is the slope and b is the Y-intercept. The tutorial then demonstrates how to calculate the slope using two points on the line and subsequently find the Y-intercept through algebraic manipulation. The process involves substituting known values into the equation and solving for the Y-intercept, which is confirmed to be 2 and 2/3.

What is the Y-intercept of a line?

• The midpoint of the line

• The point where the line crosses the X-axis

• The point where the line crosses the Y-axis

• The slope of the line

Which part of the line equation Y = mx + b represents the slope?

• b

• Y

• x

• m

How can the slope of a line be calculated?

• By adding the change in Y to the change in X

• By multiplying the change in Y by the change in X

• By dividing the change in X by the change in Y

• By dividing the change in Y by the change in X

What is the slope of the line given the points (4, 0) and (7, -2)?

• 3/2

• -3/2

• -2/3

• 2/3

What is the first step in solving for the Y-intercept using the line equation?

• Find the midpoint of the line

• Substitute a point into the equation

• Calculate the slope

• Graph the line

When substituting the point (-2, 4) into the equation, what is the value of Y?

• -2

• 4

• 2

• 0

What is the final calculated Y-intercept of the line?

• 1 and 1/3

• 2

• 3

• 2 and 2/3

How is the Y-intercept expressed as a fraction?

• 2/3

• 8/3

• 4/3

• 12/3

What does the Y-intercept represent in the context of a graph?

• The starting point of the line on the Y-axis

• The intersection with the X-axis

• The steepness of the line

• The highest point on the graph

Why is it important to verify the slope calculation?

• To check the correctness of the graph

• To confirm the accuracy of the Y-intercept

• To ensure the line is straight

• To validate the coordinates of the points