Slope

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line, and is calculated as the change in y divided by the change in x (rise over run).

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

What is the formula to 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 positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y 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 x increases, y decreases, meaning the line falls from left to right.

Front

What is the slope of the line represented by the equation y = mx + b?

Back

The slope of the line is represented by 'm' in the equation y = mx + b.

Front

How do you graph the equation 2x + 4y = 4?

Back

To graph, convert to slope-intercept form (y = mx + b) by isolating y: 4y = -2x + 4, then y = -1/2x + 1.

Front

What is the slope of the line that passes through the points (10, 1) and (5, 2)?

Back

The slope is -1/5.

Front

What is the slope of the line that passes through the points (-4, 7) and (-6, -4)?

Back

The slope is 11/2.

Front

What is the significance of the y-intercept in a linear equation?

Back

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