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 of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope means it rises, negative slope means it falls).

Front

How do you calculate the slope (m) between two points (x1, y1) and (x2, y2)?

Back

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

Front

Find the slope of the line that passes through the points (1, 2) and (3, 6).

Back

m = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How can you determine if two lines are parallel?

Back

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

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

Convert the equation y = 2x + 3 to standard form.

Back

The standard form is -2x + y = 3.

Front

What does it mean for a line to be perpendicular to another line?

Back

Two lines are perpendicular if the product of their slopes is -1. If one line has a slope of m, the other line's slope will be -1/m.

Front

Find the slope of the line that is perpendicular to the line with slope 3.

Back

The slope of the perpendicular line is -1/3.