Slope Constant Rate Linear Equations

What does 'b" represent in y=mx+b

• y-intercept

• macaroni

• nothing

• slope

Does the table above represent a proportional or non-proportional relationship?

• Proportional

• Non-Proportional

In this relationship, when one quantity changes by a certain amount, the other quantity always changes by a set amount. In this relationship, one quantity has a constant rate of change with respect to the other. Its graph is a line.

• linear relationship

• proportional relationship

• rate of change

• exponential relationship

Answer explanation

A linear relationship between two quantities means they are related like this: When one quantity changes by a certain amount, the other quantity always changes by a set amount. In a linear relationship, one quantity has a constant rate of change with respect to the other.

The relationship is called linear because its graph is a line.

The graph shows a relationship between number of days and number of pages read. When the number of days increases by 2, the number of pages read always increases by 60. The rate of change is constant, 30 pages per day, so the relationship is linear.

A number we can calculate using any two points on the line. To find it, you would divide the vertical distance between the points by the horizontal distance.

Answer explanation

The slope of a line is a number we can calculate using any two points on the line. To find the slope, divide the vertical distance between the points by the horizontal distance.

The slope of this line is 2 divided by 3 or 2/3.

The amount y changes when x increases by 1. Also called the slope.

• slope

• linear

• rate of change

• origin

Answer explanation

The rate of change in a linear relationship is the amount y changes when x increases by 1. The rate of change in a linear relationship is also the slope of its graph.

In this graph, y increases by 15 dollars when x increases by 1 hour. The rate of change is 15 dollars per hour.

• linear relationship

• slope

• ratio

• constant of proportionality

Answer explanation

In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity. This number is called the constant of proportionality.

In this example, the constant of proportionality is 3, because 2⋅3=6, 3⋅3=9, and 5⋅3=15. This means that there are 3 apples for every 1 orange in the fruit salad.

A relationship in which the values for one quantity are each multiplied by the same number to get the values for the other quantity.

• proportional relationship

• linear relationship

• constant of proportionality

• linear equation

Answer explanation

In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity.

For example, in this table every value of p is equal to 4 times the value of s on the same row. We can write this relationship as p=4s. This equation shows that s is proportional to p.

Which equations represent linear functions?

• Equations 1 and 2, only

• Equations 1 and 4, only

• Equations 2 and 3, only

• Equations 1, 3, and 4, only

Find the slope

• -5/3

• -3/5

• 5/3

• 3/5

Find the slope of the line.

• -5/4

• 5/4

• -4/5

• 4/5