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 the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept (b) in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How do you find the slope between 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 equation of a line with a slope of 2 and a y-intercept of -3?

Back

The equation is y = 2x - 3.

Front

If a line passes through the points (2, 3) and (4, 7), what is the slope?

Back

The slope is 2, calculated as (7 - 3) / (4 - 2).

Front

What does it mean if the slope of a line is negative?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line goes down from left to right.

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, and A should be non-negative.

Front

How can you convert the equation y = 3x + 2 to standard form?

Back

To convert to standard form, rearrange it to -3x + y = 2 or 3x - y = -2.

Front

What is the significance of the point (0, b) in a linear equation?

Back

The point (0, b) is the y-intercept, indicating where the line crosses the y-axis.