Linear Functions and Their Properties

This video tutorial covers the basics of linear functions and proportionality, focusing on the equation y = mx + b. It explains how to convert word problems into equations and solve them, using T-charts and examples. The tutorial also provides homework help and practical examples to reinforce the concepts taught.

What is the general form of a linear function?

• y = ax^2 + bx + c

• y = x^2 + y^2 = r^2

• y = mx + b

• y = a/x

In the equation y = mx + b, what does 'm' represent?

• The y-intercept

• The slope

• The x-intercept

• The constant term

If Joe fills a pot at 8 cups per minute, how long will it take to fill a 100-cup pot?

• 20 minutes

• 10 minutes

• 12.5 minutes

• 15 minutes

What is the slope of a line if the T-chart shows a change from 0 to 16 dollars over 4 days?

• 2 dollars per day

• 5 dollars per day

• 3 dollars per day

• 4 dollars per day

How do you find the slope of a line using two points?

• Subtract the x-values and divide by the y-values

• Subtract the y-values and divide by the x-values

• Add the x-values and y-values

• Multiply the x-values and y-values

If a linear equation is y = 13x + 98, what is the y-intercept?

• 98

• 13

• x

• 0

What does a constant rate imply in a word problem?

• An exponential function

• A logarithmic function

• A quadratic function

• A linear function

If Joey and Chloe wrap gifts at a rate of 3 gifts per minute, how many gifts will they have wrapped after 14.7 minutes?

• 70 gifts

• 60 gifts

• 50 gifts

• 44 gifts

In a sideways T-chart, what is the first step to find the equation of a line?

• Find the y-intercept

• Find the slope

• Find the x-intercept

• Find the midpoint

What is the equation of a line if the slope is 6 and the y-intercept is 10?

• y = 6x + 10

• y = 10x - 6

• y = 10x + 6

• y = 6x - 10