Chpt 3,TEST: L1-3: ROC/Slope / y=mx Form

Front

What does it mean for a quantity to be directly proportional to another?

Back

A quantity is directly proportional to another if it increases or decreases at a constant rate. For example, if you earn $70 for 5 hours of work, you earn $14 for each hour worked.

Front

How do you calculate the total earnings based on hours worked when given a rate?

Back

To calculate total earnings, multiply the rate of pay by the number of hours worked. For example, if the rate is $14 per hour and you work 22 hours, total earnings = 14 * 22 = $308.

Front

What is the rate of change in a linear relationship?

Back

The rate of change is the amount by which one quantity changes in relation to another. It is often represented as 'rise over run' in a graph.

Front

How do you find the slope of a line given two points?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the slope of the line that passes through the points (1, 6) and (-3, 7)?

Back

The slope is -1/4.

Front

What does a slope of -1/4 indicate about a line?

Back

A slope of -1/4 indicates that for every 4 units you move to the right on the x-axis, the line moves down 1 unit on the y-axis.

Front

What is the meaning of a positive slope?

Back

A positive slope indicates that as one variable increases, the other variable also increases, showing a direct relationship.

Front

What is the meaning of a negative slope?

Back

A negative slope indicates that as one variable increases, the other variable decreases, showing an inverse relationship.

Front

How can you interpret the slope in a real-world context?

Back

In a real-world context, the slope can represent rates, such as speed or cost per unit. For example, a slope of $20 each week means that for each week, the amount increases by $20.

Front

What is the formula for the slope-intercept form of a line?

Back

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