Understanding Linear Relationships and Slope

This lesson covers the equation y = mx + b, focusing on understanding the slope (m) and intercept (b). It explains how to identify and graph proportional and non-proportional relationships, calculate slope, and write equations. The lesson uses examples like snow accumulation to illustrate these concepts.

What does the 'm' in the equation y = mx + b represent?

• The slope

• The x-intercept

• The constant term

• The y-intercept

In a proportional relationship, what does the constant 'k' represent?

• The y-intercept

• The slope

• The total change

• The x-intercept

If a graph shows a proportional relationship, where does the line pass through?

• The origin

• The point (1,1)

• The y-axis

• The x-axis

How do you calculate the slope of a line?

• Divide the change in y by the change in x

• Subtract the change in x from the change in y

• Multiply the change in y by the change in x

• Add the change in y to the change in x

What is the slope of a line if the change in y is 1 and the change in x is 2?

• 1/2

• 2

• 0

• 1

What distinguishes a non-proportional relationship from a proportional one?

• It has no y-intercept

• It has a constant rate of change

• It does not pass through the origin

• It has a slope of zero

In the equation y = mx + b, what does 'b' represent in a non-proportional relationship?

• The rate of change

• The y-intercept

• The x-intercept

• The slope

How do you find the y-intercept of a line?

• By setting y to zero in the equation

• By setting x to zero in the equation

• By dividing y by x

• By finding the slope

What is the equation of a line with a slope of 1/2 and a y-intercept of 5?

• y = 1/2x + 5

• y = 5x + 1/2

• y = 1/2x - 5

• y = 5x - 1/2

If a line has a slope of 1/2 and passes through the point (4, 7), what is the y-intercept?

• 5

• 3

• 1

• 7