Graphing Linear Equations

Front

What is the general equation of a linear equation?

Back

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 represents the rate of change of y with respect to x, indicating how steep the line is.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

How do you determine 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 standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are integers.

Front

How can you convert the standard form of a linear equation to slope-intercept form?

Back

Rearrange the equation to solve for y: y = (-A/B)x + (C/B).

Front

What is the significance of parallel lines in graphing linear equations?

Back

Parallel lines have the same slope but different y-intercepts, meaning they never intersect.

Front

What is the significance of perpendicular lines in graphing linear equations?

Back

Perpendicular lines have slopes that are negative reciprocals of each other, meaning m1 * m2 = -1.

Front

How can you graph a linear equation using the slope and y-intercept?

Back

Start at the y-intercept (0, b) on the y-axis, then use the slope (rise/run) to find another point.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, defined by a linear equation.