Perpendicular and Parallel Lines

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 equation of a line (y = mx + b). It is calculated as the rise over run, or the change in y divided by the change in x.

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 'b' in the equation of a line (y = mx + b). It can be found by setting x to 0 in the equation.

Front

How do you find the slope from an equation in standard form?

Back

To find the slope from an equation in standard form (Ax + By = C), rearrange it into slope-intercept form (y = mx + b) by solving for y.

Front

What is the relationship between parallel lines?

Back

Parallel lines have the same slope but different y-intercepts. They never intersect.

Front

What is the relationship between perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other. If one line has a slope of m, the other will have a slope of -1/m.

Front

Write the equation of a line parallel to y = 2x + 1 through the point (1, 3).

Back

y = 2x + 1.

Front

Write the equation of a line perpendicular to y = -3x + 2 through the point (2, 1).

Back

y = 1/3x + 5/3.

Front

What is the slope of the line represented by the equation y = 5x - 4?

Back

The slope is 5.

Front

What is the slope of the line represented by the equation y = -2x + 7?

Back

The slope is -2.

Front

If two lines have slopes of 1/2 and -2, are they parallel, perpendicular, or neither?

Back

They are perpendicular because their slopes are negative reciprocals.