All Forms of Linear Equations

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 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

Convert the slope-intercept form y = mx + b to standard form.

Back

To convert to standard form, rearrange to Ax + By = C, where A, B, and C are integers.

Front

What is the slope of the line represented by the equation 3x + 4y = 12?

Back

The slope is -3/4, found by rearranging to slope-intercept form.

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 y when x = 0.

Front

Write the equation of a line in standard form that passes through the point (1, 2) with a slope of 3.

Back

The equation is 3x - y = 1.

Front

What is the significance of the coefficients in the standard form of a linear equation?

Back

The coefficients A and B determine the slope and direction of the line.

Front

How do you find the x-intercept of a linear equation?

Back

Set y = 0 in the equation and solve for x.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have equal slopes.