Slope & Intercepts

Front

What is the definition of slope?

Back

Slope is a measure of the steepness 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

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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

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 does a slope of zero mean?

Back

A slope of zero means that the line is horizontal and there is no vertical change as the x-value changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in a vertical line where the x-value does not change, resulting in a division by zero when calculating slope.

Front

If a line has a slope of 1/2, what does this mean in practical terms?

Back

This means that for every 2 units you move horizontally to the right, the line rises 1 unit vertically.

Front

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

Back

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

Front

What is the y-intercept in the equation y = 3x + 4?

Back

The y-intercept is 4, which is the point where the line crosses the y-axis.

Front

How can you identify the slope from a graph?

Back

The slope can be identified by selecting two points on the line, calculating the rise over run between them.