Writing Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does 'm' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line, which indicates the steepness and direction of the line.

Front

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

Back

In the equation y = mx + b, 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line represented by the equation y = 3x + 9?

Back

The slope of the line is 3.

Front

What is the y-intercept of the line represented by the equation y = 3x + 9?

Back

The y-intercept of the line is 9.

Front

How do you write a linear equation given a slope and a point?

Back

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

Front

What is the equation of a line with a slope of -5 that passes through the point (2, 3)?

Back

Using the point-slope form, the equation is y - 3 = -5(x - 2), which simplifies to y = -5x + 13.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.

Front

How do you convert the equation y = 2x + 4 to standard form?

Back

Rearranging gives -2x + y = 4, or 2x - y = -4.