Linear Equations Flashcard Review Topic 2

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 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.

Front

What is point-slope form of a linear equation?

Back

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

Front

How do you convert the equation 3x + y = 5 to slope-intercept form?

Back

To convert to slope-intercept form, solve for y: y = -3x + 5.

Front

What is the y-intercept of the equation 2x + 3y = 6?

Back

To find the y-intercept, set x = 0: 3y = 6, so y = 2. The y-intercept is (0, 2).

Front

What is the x-intercept of the equation 4x - 2y = 8?

Back

To find the x-intercept, set y = 0: 4x = 8, so x = 2. The x-intercept is (2, 0).

Front

How do you determine if a line is increasing or decreasing based on its slope?

Back

A line is increasing if the slope is positive and decreasing if the slope is negative.

Front

What is the formula for finding the equation of a line given a point and a slope?

Back

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