Slope and Y-Intercept

Front

What is the definition of 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, where b is the y-intercept.

Front

How do you find the slope of a line given 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 the x-value increases, the y-value 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 the x-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no change in the y-value as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it would require division by zero when calculating the slope.

Front

How can you determine the y-intercept from a linear equation in slope-intercept form?

Back

In the slope-intercept form y = mx + b, the y-intercept is the value of b.

Front

What is the relationship between the slope and the steepness of a line?

Back

The greater the absolute value of the slope, the steeper the line. A slope of 1 is less steep than a slope of 3.

Front

How can you graph a linear equation using the slope and y-intercept?

Back

Start at the y-intercept on the y-axis, then use the slope to determine the rise over run to plot additional points.

Front

What is the formula for 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.