y-intercept and slope

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you find the y-intercept from an equation?

Back

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

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

How is slope calculated between two points (x1, y1) and (x2, y2)?

Back

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

Front

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

Back

The slope is 3.

Front

What is the y-intercept of the equation y = -2x + 5?

Back

The y-intercept is 5.

Front

If a line has a slope of 0, what does that indicate?

Back

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

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 equation of a line with a slope of 4 and a y-intercept of -1?

Back

The equation is y = 4x - 1.

Front

How can you determine if a line is increasing or decreasing based on its slope?

Back

If the slope is positive, the line is increasing; if the slope is negative, the line is decreasing.