Functions: Warmups Part 1

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph, where one variable is a constant multiple of the other plus a constant (y = mx + b).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

Front

How does the slope of a line affect its steepness?

Back

The slope of a line (m) indicates how steep the line is; a larger absolute value of the slope means a steeper line.

Front

What does it mean if one line is steeper than another in a graph?

Back

If one line is steeper than another, it indicates that the variable represented on the y-axis changes more rapidly with respect to the variable on the x-axis.

Front

How can you determine the total amount saved over time in a linear savings model?

Back

In a linear savings model, the total amount saved can be calculated using the formula: Total Savings = Initial Amount + (Savings Rate * Time).

Front

What is the significance of the initial amount in a savings scenario?

Back

The initial amount is the starting value before any additional savings are added, affecting the y-intercept of the graph.

Front

How do you interpret the slope in a context of spending money?

Back

In the context of spending money, the slope represents the rate at which money is spent per visit or transaction.

Front

What does it mean for two lines to have the same slope?

Back

If two lines have the same slope, they increase or decrease at the same rate, indicating a similar relationship between the variables.

Front

How can you compare two linear equations graphically?

Back

You can compare two linear equations graphically by plotting them on the same graph and observing their slopes and y-intercepts.

Front

What is the formula for a linear equation in slope-intercept form?

Back

The formula for a linear equation in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.