Linear Equations Flashcard

Front

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

Back

The slope of a line represents the rate of change of one variable with respect to another. For example, in the context of a swimming pool, it indicates how many inches of water are added per hour.

Front

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

Back

The slope (m) can be 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 a direct variation, and how is it represented mathematically?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other. It is represented mathematically as y = kx, where k is a non-zero constant.

Front

If a jet travels 1,350 miles in 3 hours, what is its speed in miles per hour?

Back

The speed is calculated as distance/time, so the speed is 1,350 miles / 3 hours = 450 miles per hour.

Front

What is a function in mathematical terms?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

Front

How can you determine if a set of ordered pairs represents a function?

Back

A set of ordered pairs represents a function if no x-value is repeated with a different y-value.

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

How do you interpret the slope of a line in a graph?

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables. A positive slope indicates a direct relationship, while a negative slope indicates an inverse relationship.

Front

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

Back

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

Front

In the context of a balloon rising, how would you express its height as a function of time?

Back

The height of the balloon can be expressed as h(t) = mt + b, where m is the rate of rise and b is the initial height.