Standard Form and Parallel/Perpendicular Lines Review

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you convert the slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms involving x and y on one side and the constant on the other.

Front

What are the x and y intercepts of a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis (y=0), and the y-intercept is the point where the line crosses the y-axis (x=0).

Front

How do you find the x-intercept of the equation x - 3y = 6?

Back

To find the x-intercept, set y = 0 and solve for x. For x - 3(0) = 6, x = 6, so the x-intercept is (6, 0).

Front

How do you find the y-intercept of the equation x - 3y = 6?

Back

To find the y-intercept, set x = 0 and solve for y. For 0 - 3y = 6, y = -2, so the y-intercept is (0, -2).

Front

What is the slope of the line represented by the equation 2x - 3y = 12?

Back

To find the slope, rearrange the equation to slope-intercept form (y = mx + b). The slope (m) is 2/3.

Front

What is the y-intercept of the line represented by the equation 2x - 3y = 12?

Back

The y-intercept (b) can be found by rearranging the equation to slope-intercept form. For 2x - 3y = 12, the y-intercept is -4.

Front

How can you determine if two lines are parallel?

Back

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

Front

How can you determine if two lines are perpendicular?

Back

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

Front

What does it mean for two lines to be coinciding?

Back

Two lines are coinciding if they lie on top of each other, meaning they have the same slope and y-intercept.