Determining Slope and y-Intercept Mastery

The video tutorial covers the concepts of slope and y-intercept in linear equations. It explains how to calculate the slope using points on a graph and the significance of the y-intercept. The tutorial also discusses the rate of change and initial value in linear equations, using examples from tables to find these values. Additionally, it derives the slope-intercept form of a line, providing a comprehensive understanding of these fundamental concepts in algebra.

What does the slope of a line represent?

• The point where the line crosses the x-axis

• The steepness and direction of the line

• The length of the line

• The point where the line crosses the y-axis

How do you calculate the slope between two points?

• Subtract the x-coordinates from the y-coordinates

• Divide the difference in y-coordinates by the difference in x-coordinates

• Add the x-coordinates and y-coordinates

• Multiply the x-coordinates and y-coordinates

What is the slope of the line passing through the points (0, 4) and (-3, 6)?

• 2/3

• -2/3

• 3/2

• -3/2

What is the y-intercept of the line represented by the equation y = -2/3x + 4?

• (0, -2/3)

• (0, 4)

• (4, 0)

• (4, -2/3)

In the context of a linear equation, what does the 'b' in y = mx + b represent?

• The slope of the line

• The x-intercept

• The y-intercept

• The rate of change

If a salesperson sells 10 phones and earns $480, and sells 20 phones and earns $630, what is the rate of change in their earnings?

• $10 per phone

• $15 per phone

• $20 per phone

• $25 per phone

What is the initial value or base salary of the salesperson if they sell 0 phones?

• $330

• $150

• $630

• $480

How do you find the y-intercept from a table of values?

• Look for the y-value when x is 0

• Look for the x-value when y is 0

• Find the average of all y-values

• Find the average of all x-values

What is the slope of the line passing through the points (2, 4) and (4, 14)?

• 3

• 2

• 5

• 4

If a line has a slope of 5 and passes through the point (0, 12), what is its equation in slope-intercept form?

• y = 5x + 12

• y = 12x + 5

• y = 5x - 12

• y = 12x - 5