check for understanding graphing line with slope and point

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness of a line, calculated as the rise (change in y) over the run (change in x).

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

Slope (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-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 is the y-intercept of a line?

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 graph a line given a slope and a point?

Back

Start at the given point, then use the slope to determine the rise and run to find another point, and draw the line through both points.

Front

What is the significance of the point (0, b) in a linear equation?

Back

The point (0, b) is the y-intercept, indicating where the line crosses the y-axis.

Front

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

Back

For every 2 units the line rises, it runs 3 units to the right.

Front

How can you determine if a line is vertical or horizontal?

Back

A vertical line has an undefined slope (x = constant), while a horizontal line has a slope of 0 (y = constant).