Lines in Context

Front

What does the y-intercept represent?

Back

The y-intercept represents the value of y when x is 0, indicating the starting point of a linear function on the y-axis.

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 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 does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Front

What is the slope of the line represented by the equation y = -1.5x + 4?

Back

The slope of the line is -1.5.

Front

What is the y-intercept of the line represented by the equation y = 3x + 8?

Back

The y-intercept of the line is 8.

Front

How can you determine the y-intercept from a graph?

Back

The y-intercept can be determined by finding the point where the line crosses the y-axis.

Front

What does the term 'linear function' mean?

Back

A linear function is a function that graphs to a straight line, defined by the equation y = mx + b.

Front

What is the significance of the slope in real-world contexts?

Back

The slope represents the rate of change, such as speed, cost per item, or growth rate.