Linear Equations Review

Front

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

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

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

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

Back

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

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 (m1 * m2 = -1).

Front

How do you convert the standard form of a linear equation (Ax + By = C) to slope-intercept form?

Back

Solve for y to get y = (-A/B)x + (C/B).

Front

What is the significance of the point (0, b) in the slope-intercept form?

Back

The point (0, b) is the y-intercept of the line, indicating where the line crosses the y-axis.

Front

How can you determine if a point lies on a line represented by an equation?

Back

Substitute the x-value of the point into the equation and check if the resulting y-value matches the y-value of the point.

Front

What is the formula for finding the y-intercept from a linear equation in standard form?

Back

Set x = 0 in the equation Ax + By = C to find the y-intercept (0, C/B).