What is a linear equation?

A linear equation is an equation of the first degree, meaning it involves only the first power of the variable(s). 
It can be expressed in the form ax + b = c, where a, b, and c are constants, and x is the variable.

How do you solve the linear equation 3x + 5 = 20?

To solve for x, 
first subtract 5 from both sides: 3x = 15. 
Then, divide both sides by 3: x = 5.

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

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

If a linear equation is given as 2y - 4x = 8, how do you convert it to slope-intercept form?

To convert to slope-intercept form, 
solve for y: 2y = 4x + 8, 
then divide by 2: y = 2x + 4. 
Here, the slope (m) is 2 and the y-intercept (b) is 4.

Determine the x-intercept of the linear equation 4x + 2y = 8.

To find the x-intercept, 
set y = 0: 4x + 2(0) = 8, 
which simplifies to 4x = 8. 
Dividing both sides by 4 gives x = 2. 
Thus, the x-intercept is (2, 0).

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

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

What does the coefficient 'm' represent in the slope-intercept form?

In the slope-intercept form y = mx + b, the coefficient 'm' represents the slope of the line, indicating the rate of change of y with respect to x.

How can you eliminate fractions from a linear equation?

To eliminate fractions from a linear equation, multiply both sides of the equation by a common denominator. This process will clear the fractions and make the equation easier to solve.

What is the standard form of a linear equation?

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

Solve the equation 5x - 3 = 2x + 6 for x.

First, subtract 2x from both sides: 3x - 3 = 6. 
Then add 3 to both sides: 3x = 9. 
Finally, divide by 3: x = 3.

If the slope of a line is 3 and it passes through the point (1, 2), what is the equation of the line in point-slope form?

Using the point-slope form y - y₁ = m(x - x₁), we substitute: y - 2 = 3(x - 1). This gives the equation y - 2 = 3x - 3, or y = 3x - 1.

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

To find the y-intercept, set x = 0 in the equation: 2(0) + 3y = 6, 
which simplifies to 3y = 6. 
Dividing by 3 gives y = 2. 
Thus, the y-intercept is (0, 2).

What do the solutions of a system of linear equations represent?

The solutions of a system of linear equations represent the points where the lines intersect. This point is the common solution for both equations.

What is the elimination method for solving a system of linear equations?

The elimination method involves manipulating the equations to eliminate one variable, allowing you to solve for the other variable. This is done by adding or subtracting the equations after making the coefficients of one variable the same.

If a linear equation has no solution, what does this imply about its graph?

If a linear equation has no solution, this implies that the lines represented by the equations are parallel and will never intersect.