Comparing linear equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for two quantities to have a proportional relationship?

Back

Two quantities have a proportional relationship if they maintain a constant ratio. This means that as one quantity increases or decreases, the other does so in a consistent manner.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run). It indicates how much y changes for a unit change in x.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented as (0, b) in the equation y = mx + b.

Front

How can you determine if a relationship is linear from a graph?

Back

A relationship is linear if the graph forms a straight line. If the points on the graph can be connected with a straight line, the relationship is linear.

Front

What is the intersection point of two lines?

Back

The intersection point of two lines is the point where they cross each other. This point represents the solution to the system of equations represented by the two lines.

Front

How do you find the cost at which two gym memberships are equal?

Back

To find the cost at which two gym memberships are equal, set the equations for both memberships equal to each other and solve for the variable.

Front

What does it mean if a gym membership is modeled by the equation Cost = 75m?

Back

This means that the cost of the gym membership increases by $75 for each month (m) of membership.

Front

What is the significance of the point (0, 100) in the context of NYSC's membership?

Back

The point (0, 100) indicates that at month 0 (the start), the cost of NYSC's membership is $100.

Front

What is the difference between proportional and linear relationships?

Back

A proportional relationship passes through the origin (0,0) and has a constant ratio, while a linear relationship can have a y-intercept that is not zero.