Slope from equations

Front

What is the definition of slope in a linear equation?

Back

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

Front

How do you determine if a slope is positive, negative, or zero?

Back

A slope is positive if the line rises from left to right, negative if it falls from left to right, and zero if the line is horizontal.

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 does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal and there is no vertical change as x changes.

Front

What does a positive slope indicate about the relationship between x and y?

Back

A positive slope indicates that as x increases, y also increases.

Front

What does a negative slope indicate about the relationship between x and y?

Back

A negative slope indicates that as x increases, y decreases.

Front

How can you find the slope from two points on a line?

Back

The slope 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 the slope of the line represented by the equation y = 3x + 5?

Back

The slope of the line is 3.

Front

If a line has a slope of -2, what does this tell you about the line's direction?

Back

The line is decreasing, meaning it falls from left to right.

Front

What is the significance of the y-intercept in the slope-intercept form?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.