Linear Equations and Their Properties

The video tutorial covers understanding and interpreting linear equations, finding points on a line using slope, deriving linear functions from data points, solving for unknowns in equations, and interpreting cost equations in real-world scenarios. It emphasizes the importance of slope and y-intercept in graph interpretation and provides practical examples to illustrate these concepts.

What is the y-intercept of a line if it touches the y-axis at 20?

• 20

• 10

• 0

• 30

If a line has a slope of 0.05, what does this represent in terms of rise over run?

• 10 over 200

• 5 over 100

• 0.5 over 10

• 1 over 20

A line passes through the origin with a slope of 2/3. Which point lies on this line?

• (4, 6)

• (2, 3)

• (6, 4)

• (3, 2)

How do you find the next point on a line with a slope of 2/3 starting from the origin?

• Rise 3, run 2

• Rise 2, run 3

• Run 3, rise 2

• Run 2, rise 3

Given points (4, 1) and (6, 4), what is the slope of the line?

• 2/3

• 3/2

• 1/2

• 4/3

What is the equation of a line passing through (4, 1) with a slope of 3/2?

• y = 3/2x + 1

• y = 3/2x - 5

• y = 2/3x + 1

• y = 2/3x - 5

If a line passes through the origin and points (3, b) and (b, 48), what is the value of b?

• 48

• 36

• 24

• 12

What is the square root of 144, which is used to find the value of b in the equation?

• 12

• 13

• 11

• 10

In the equation c = 0.15m + 2.25, what does the 0.15 represent?

• Cost per minute

• Total cost

• One-time service fee

• Discount rate

What is the one-time service fee in the equation c = 0.15m + 2.25?

• 225

• 15

• 2.25

• 0.15