All Forms of Linear Equations

Front

What is the point-slope form of a linear equation?

Back

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you find the slope of a line given two points?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

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 from 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 on one side.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

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

Front

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

Back

The y-intercept can be found by setting x = 0 in the equation and solving for y.

Front

What is the slope of the line represented by the equation 2x - 3y = 6?

Back

To find the slope, rearrange to slope-intercept form: y = (2/3)x - 2, so the slope is 2/3.

Front

How do you write the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), substituting the slope (m) and the coordinates of the point (x1, y1).

Front

What is the relationship between the slopes of parallel lines?

Back

The slopes of parallel lines are equal.