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 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 isolate the variables on one side.

Front

What is the slope of a line?

Back

The slope of a line (m) is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

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

Back

The y-intercept is the value of y when x = 0. It can be found by substituting x = 0 into the equation.

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, meaning they intersect at a right angle.

Front

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

Back

The slope (m) can be 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 formula for the point-slope form of a linear equation?

Back

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

Front

How do you write an equation for a line given a point and a slope?

Back

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

Front

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

Back

In the standard form Ax + By = C, A, B, and C are integers, and A should be non-negative. The coefficients A and B determine the slope of the line.