Equations of Parallel and Perpendicular 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'. It is calculated as the change in y divided by the change in x (rise over run).

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

How do you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the slope-intercept form of a line?

Back

The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

Convert the equation y = -6x + 3 to standard form.

Back

The standard form is 6x + y = 3.

Front

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

Back

The y-intercept is 5, which is the value of y when x = 0.

Front

Find the slope of the line passing through the points (2, 3) and (4, 7).

Back

The slope m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

Write the equation of a line in slope-intercept form that has a slope of -3 and passes through the point (1, 2).

Back

The equation is y = -3x + 5.

Front

What are the x and y intercepts of the equation 2x + 3y = 6?

Back

The x-intercept is 3 (when y=0) and the y-intercept is 2 (when x=0).

Front

If a line has a slope of 1/2, what is the slope of a line parallel to it?

Back

The slope of a parallel line is also 1/2.