Slope from a Graph

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change (rise) to the horizontal change (run).

Front

How do you calculate the slope from 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 is the slope of a horizontal line?

Back

The slope of a horizontal line is zero.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

What is the slope of a line that goes through the points (2, 3) and (4, 7)?

Back

Slope = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

What does it mean if a line has a slope of 1/2?

Back

It means for every 2 units you move horizontally to the right, you move 1 unit up vertically.

Front

What is the relationship between slope and steepness?

Back

A larger absolute value of slope indicates a steeper line, while a smaller absolute value indicates a gentler slope.

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.