Linear Review

Front

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

Back

The point-slope form is given by the equation 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 is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you convert from point-slope form to slope-intercept form?

Back

To convert, solve for y in the point-slope form equation y - y1 = m(x - x1) to get y = mx + (y1 - mx1).

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How do you determine if a point lies on a line given its equation?

Back

Substitute the x and y coordinates of the point into the equation. If the equation holds true, the point lies on the line.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

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

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts.

Front

What is the relationship between perpendicular lines in terms of slope?

Back

Perpendicular lines have slopes that are negative reciprocals of each other, meaning if one slope is m, the other is -1/m.