Understanding Linear Relationships and Slopes

The video tutorial explains the concept of linear relationships, focusing on the rate of change, which is constant in linear data. It introduces the concept of slope as the ratio of vertical change to horizontal change, also known as rise over run. The tutorial provides examples of calculating slope using a graph, demonstrating both positive and negative slopes. It concludes with practice problems for viewers to apply the concepts learned.

What is the relationship between time and distance in a linear graph?

• The relationship is quadratic.

• The relationship is logarithmic.

• The relationship is exponential.

• The relationship is linear.

What does a constant rate of change in a linear graph indicate?

• The graph is a circle.

• The graph is a parabola.

• The graph is a straight line.

• The graph is a curve.

How is the slope of a line defined?

• Horizontal change over vertical change.

• Sum of vertical and horizontal changes.

• Difference between vertical and horizontal changes.

• Vertical change over horizontal change.

What is another term for the slope of a line?

• Gradient

• Intercept

• Vertex

• Axis

In the example of a positive slope, what is the rise and run between the points (-2, -1) and (1, 1)?

• Rise: 3, Run: 2

• Rise: 2, Run: 1

• Rise: 2, Run: 3

• Rise: 1, Run: 2

What is the slope of the line in the positive slope example?

• 1/2

• 2/1

• 3/2

• 2/3

In the example of a negative slope, what is the rise and run between the points (-3, 2) and (2, -2)?

• Rise: 5, Run: -4

• Rise: -5, Run: 4

• Rise: 4, Run: -5

• Rise: -4, Run: 5

What is the slope of the line in the negative slope example?

• -5/4

• 4/5

• -4/5

• 5/4

How does a line with a positive slope appear on a graph?

• Slants downward from left to right

• Slants upward from left to right

• Is horizontal

• Is vertical

How does a line with a negative slope appear on a graph?

• Is vertical

• Slants downward from left to right

• Slants upward from left to right

• Is horizontal