Multiple Representations Card Sort

Front

What does the equation y = 7.5x - 3 represent in a real-world context?

Back

It represents a situation where Benji spent $3 on art supplies and sells paintings for $7.50 each, calculating his profit.

Front

What is the equation for a candle that burns at a rate of 1.5 inches per hour?

Back

y = -1.5x + 12, where y is the height of the candle and x is the time in hours.

Front

Which equation corresponds to a graph with a negative slope that crosses the y-axis at 5?

Back

y = -3x + 5.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the total amount in a savings account after m months if you start with $50 and deposit $75 each month?

Back

t = 75m + 50.

Front

What does the slope of a line represent in a real-world scenario?

Back

The slope represents the rate of change or how much one quantity changes in relation to another.

Front

What is the y-intercept in the equation y = 2/3x + 1?

Back

The y-intercept is 1, which is the value of y when x = 0.

Front

How can you determine if a linear equation is increasing or decreasing?

Back

If the slope (m) is positive, the line is increasing; if negative, the line is decreasing.

Front

What does the term 'linear equation' mean?

Back

A linear equation is an equation that makes a straight line when graphed, typically in the form y = mx + b.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients determine the slope and y-intercept, affecting the line's steepness and position.