Forms of 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 (positive slope goes up, negative slope goes down).

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 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 point-slope form of a linear equation?

Back

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

Front

Convert the equation y = 2x + 3 to slope-intercept form.

Back

The equation is already in slope-intercept form, where the slope (m) is 2 and the y-intercept (b) is 3.

Front

What are the x and y intercepts of the equation 2x + 3y = 6?

Back

The x-intercept is 3 (when y=0) and the y-intercept is 2 (when x=0).

Front

How do you write an equation in standard form?

Back

An equation is in standard form if it is written as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope. If two lines are parallel, their slopes (m) are equal.

Front

What is the relationship between the slopes of perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other. If one line has a slope of m, the other line's slope will be -1/m.