Linear Equations Review

Front

What is the slope in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x.

Front

How do you interpret the slope in a real-world context?

Back

The slope indicates how much y changes for a unit change in x, often representing a rate.

Front

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

Back

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

Front

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

Back

The slope is calculated as (y2 - y1) / (x2 - x1).

Front

What is the equation of a line parallel to y = mx + b?

Back

A line parallel to y = mx + b has the same slope m but a different y-intercept.

Front

What is the equation of a line perpendicular to y = mx + b?

Back

A line perpendicular to y = mx + b has a slope of -1/m.

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).

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients determine the slope and y-intercept, defining the line's steepness and position.

Front

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

Back

Two lines are parallel if their slopes are equal; they are perpendicular if the product of their slopes is -1.

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.