Linear Equations in 2 variables

Front

What is a linear equation in two variables?

Back

A linear equation in two variables is an equation that can be expressed in the form Ax + By = C, where A, B, and C are constants, and x and y are variables.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x, indicating how much y changes for a unit change in x.

Front

How do you find the y-intercept of a linear equation?

Back

The y-intercept of a linear equation can be found by setting x = 0 in the equation and solving for y.

Front

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

Back

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

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

Front

How can you determine the slope from two points on a line?

Back

The slope can be determined using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

What is the relationship between parallel lines and their slopes?

Back

Parallel lines have the same slope, meaning they never intersect and maintain a constant distance apart.

Front

What is the relationship between perpendicular lines and their slopes?

Back

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