Graphing and Analyzing Linear Functions

The video tutorial covers various mathematical concepts for eighth-grade students. It begins with matching graphs to real-life situations, identifying independent and dependent variables, and labeling axes. The next section narrates a story about filling and draining an aquarium, illustrating changes in water level over time. The tutorial then explains how to calculate the area of a circle using the radius and pi, with examples of filling in a table of values. Finally, it demonstrates graphing linear equations by plotting points and understanding the slope, using a line equation to explore relationships between lengths and widths of rectangles.

Which graph represents a scenario where a plant grows at a constant rate every week?

• Graph D

• Graph C

• Graph B

• Graph A

What does the y-intercept represent in the graph of a carnival with an entry fee and ride costs?

• The total number of visitors

• The number of rides

• The entry fee

• The total cost of rides

In Jada's aquarium story, what happens after she fills the tank for two minutes and then stops?

• She drains the tank

• She resumes filling the tank

• She adds fish to the tank

• She cleans the tank

What is the formula for the area of a circle?

• A = 2πr

• A = πr^2

• A = 2πr^2

• A = πd

If the area of a circle is 16π, what is the radius?

• 5

• 4

• 3

• 2

What is the radius if the area of a circle is 100π?

• 9

• 11

• 8

• 10

What is the slope of the line that passes through the points (4, 8), (2, 10), and (5, 7)?

• 1

• 0

• 2

• -1

What does the slope of the line tell you about the relationship between lengths and widths of rectangles with a perimeter of 24?

• The length and width both increase

• The length and width remain constant

• For every unit added to the length, a unit is removed from the width

• For every unit added to the length, a unit is added to the width

Which point lies on the line 2x + 2y = 24?

• (5, 5)

• (6, 6)

• (4, 8)

• (3, 9)

What is the equation of the line that passes through the points (4, 8), (2, 10), and (5, 7)?

• y = -2x + 12

• y = -x + 12

• y = x + 4

• y = 2x + 4