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 or negative).

Front

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

Back

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

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

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical. This means that the x-coordinate does not change, and the equation of the line is in the form x = a constant.

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is in the form y = b, where b is the y-coordinate of any point on the line.

Front

How do you graph the equation y = 2/3x - 3?

Back

To graph y = 2/3x - 3, start at the y-intercept (0, -3) and use the slope (rise/run = 2/3) to find another point.

Front

What is the significance of the slope in the equation y = 3x - 11?

Back

In the equation y = 3x - 11, the slope is 3, which means for every 1 unit increase in x, y increases by 3 units.

Front

How can you determine if two lines are parallel?

Back

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

Front

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

Back

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