SLOPE: from Story Problem (Daily Self-Check)

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

What is the formula for calculating slope?

Back

The formula for calculating slope (m) is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What is the significance of the y-intercept 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

In the context of a story problem, how can slope be interpreted?

Back

In a story problem, slope can represent rates of change, such as speed, cost per unit, or any other quantity that changes in relation to another.

Front

What is the slope of a line that descends at a rate of 5 units per minute?

Back

The slope of a line that descends at a rate of 5 units per minute is -5.

Front

How do you determine the y-intercept from a story problem involving a fixed cost?

Back

The y-intercept can be determined as the fixed cost or initial value when the independent variable (x) is zero.

Front

What is the equation of a line in slope-intercept form?

Back

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

Front

How can you identify the slope from a word problem involving a technician's service charge?

Back

The slope can be identified as the additional charge per hour of service, which represents the rate of change in cost with respect to time.