Positive Slope

Front

What is the definition of a positive slope in a linear function?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward trend on a graph.

Front

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

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in the y-value as the x-value changes.

Front

What is the significance of a slope greater than 1?

Back

A slope greater than 1 indicates that for every unit increase in x, the y-value increases by more than one unit, resulting in a steep line.

Front

What is the significance of a slope less than 1 but greater than 0?

Back

A slope less than 1 but greater than 0 indicates that for every unit increase in x, the y-value increases by less than one unit, resulting in a gentle upward slope.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope of the line is 2, indicating a positive slope.

Front

If a line has a slope of 3/2, what does this mean in terms of rise over run?

Back

A slope of 3/2 means that for every 2 units you move to the right (run), the line rises 3 units (rise).

Front

How can you determine if a slope is positive from a graph?

Back

A slope is positive if the line rises from left to right on the graph.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero in the slope formula.

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.