Graphing Linear Equations

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you find 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 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 the y-intercept represent in a linear equation?

Back

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

Front

If a line has a slope of -5/3, what does this indicate about its direction?

Back

A slope of -5/3 indicates that the line is decreasing; for every 3 units moved to the right, the line moves down 5 units.

Front

What is the slope of a line that is horizontal?

Back

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

Front

What is the slope of a line that is vertical?

Back

The slope of a vertical line is undefined, as it would involve division by zero (change in x is 0).

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope (m).

Front

How can you determine if two lines are perpendicular using their slopes?

Back

Two lines are perpendicular if the product of their slopes is -1 (m1 * m2 = -1).

Front

Write the equation of a line with a slope of 2 and a y-intercept of 3 in slope-intercept form.

Back

The equation is y = 2x + 3.