Slope and Linear Equations

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, represented as the ratio of the rise (change in y) to the run (change in x).

Front

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

Back

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

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the slope-intercept form y = mx + b.

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 positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant 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, resulting in a downward slant from left to right.

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 horizontal line?

Back

The slope of a horizontal line is 0.

Front

If a line has a slope of 3, what does this mean?

Back

For every 1 unit increase in x, y increases by 3 units.

Front

How do you find the y-intercept from the equation y = -2x + 5?

Back

The y-intercept is 5, which is the value of y when x = 0.