Multiple Representations Card Sort

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 the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How do you interpret the equation y = -2x + 10?

Back

In this equation, the slope is -2, meaning for every 1 unit increase in x, y decreases by 2 units. The y-intercept is 10, indicating the line crosses the y-axis at (0, 10).

Front

What is the formula to calculate the total amount in a savings account after m months?

Back

The formula is t = initial amount + (monthly deposit * number of months). For Melanie, it is t = 50 + (75 * m).

Front

How do you find the depth of a submarine using the equation y = -1200x?

Back

In this equation, y represents the depth in feet, and x represents the time in hours. The negative sign indicates that the submarine is descending.

Front

What does the equation y = 2x - 5 represent?

Back

This equation represents a linear relationship where for every 1 unit increase in x, y increases by 2 units, and the line crosses the y-axis at -5.

Front

How do you calculate the total cost for attending a basketball game?

Back

The total cost t can be calculated using the equation t = 74.50n + 15, where n is the number of tickets purchased.

Front

What is a table of values in relation to a linear equation?

Back

A table of values lists pairs of x and y values that satisfy a linear equation, showing how y changes as x changes.

Front

What is the significance of the negative slope in the equation y = -2x + 5?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.