Multiple Representations

Front

What is the rate of change (m) in a linear equation?

Back

The rate of change (m) represents the slope of the line, indicating how much y changes for a unit change in x.

Front

In the equation y = mx + b, what do m and b represent?

Back

m is the slope of the line, and b is the y-intercept, the point where the line crosses the y-axis.

Front

How do you find the slope (m) from a table of values?

Back

Calculate the change in y divided by the change in x between two points: m = (y2 - y1) / (x2 - x1).

Front

Write the equation for a situation where the cost is $4 plus $3 per child, with x as the number of children.

Back

y = 3x + 4.

Front

What does the slope (m) indicate in a real-world context?

Back

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

Front

If m = 2 and b = 5, what is the equation of the line?

Back

y = 2x + 5.

Front

What is the y-intercept in the equation y = 4x + 1?

Back

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

Front

How can you represent a linear relationship using a graph?

Back

Plot points based on the equation and connect them to form a straight line.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

m = (y2 - y1) / (x2 - x1).

Front

In the equation y = 9.75x, what does 9.75 represent?

Back

9.75 is the slope (m), indicating the rate of change of y with respect to x.