Writing Linear Equations

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the rise over run, or the change in y divided by the change in x.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means that their slopes are opposite reciprocals of each other.

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 between two points?

Back

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

Front

What is the slope of a line parallel to the line y = 3x + 2?

Back

The slope of a line parallel to y = 3x + 2 is 3, as parallel lines have identical slopes.

Front

What is the slope of a line perpendicular to the line y = -4x + 1?

Back

The slope of a line perpendicular to y = -4x + 1 is 1/4, as it is the opposite reciprocal of -4.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

How can you determine if two lines are parallel from their equations?

Back

Two lines are parallel if they have the same slope (m) in their 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

What does it mean for slopes to be opposite reciprocals?

Back

Slopes are opposite reciprocals if one slope is the negative inverse of the other, meaning if one slope is m, the other is -1/m.