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 y with respect to x. It indicates how steep the line is and the direction it goes (upward or downward).

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 is the value of y when x = 0.

Front

How do you find the y-intercept from the equation y = 2x + 3?

Back

The y-intercept is 3, which means the line crosses the y-axis at the point (0, 3).

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is of the form y = k, where k is a constant. For example, y = 4 is a horizontal line.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is of the form x = k, where k is a constant. For example, x = 2 is a vertical line.

Front

How do you determine if a point lies on the line represented by the equation y = 3x - 2?

Back

Substitute the x-value of the point into the equation. If the resulting y-value matches the y-value of the point, then it lies on the line.

Front

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

Back

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

Front

How can you graph the equation y = -x + 1?

Back

Start at the y-intercept (0, 1), then use the slope (-1) to find another point by going down 1 unit and right 1 unit.

Front

What does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.