Linear Equations in Two Variables

Front

What is a linear equation in two variables?

Back

A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and x and y are variables.

Front

What does the solution of a linear equation represent?

Back

The solution of a linear equation represents the point(s) (x, y) that satisfy the equation, meaning they make the equation true.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is written as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you convert the equation y = mx + b to standard form?

Back

To convert y = mx + b to standard form, rearrange it to the form Ax + By = C by moving y to the left side and adjusting the equation accordingly.

Front

What are the x-intercept and y-intercept of a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis (y=0), and the y-intercept is where the line crosses the y-axis (x=0).

Front

If (2, 0) is a solution of the equation 2x + 3y = k, how do you find k?

Back

Substitute x = 2 and y = 0 into the equation: 2(2) + 3(0) = k, which gives k = 4.

Front

What are the coefficients in the linear equation ax + by = c?

Back

In the equation ax + by = c, a and b are the coefficients of the variables x and y, respectively.

Front

What does it mean for a linear equation to be in slope-intercept form?

Back

A linear equation is in slope-intercept form if it is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if two linear equations are parallel?

Back

Two linear equations are parallel if they have the same slope (m) but different y-intercepts (b).

Front

What is the significance of the constants a, b, and c in the equation ax + by = c?

Back

The constants a, b, and c determine the slope and position of the line represented by the equation in the coordinate plane.