P F Test 3 -- Linear Equations

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

How do you solve for a variable in a linear equation?

Back

To solve for a variable, isolate the variable on one side of the equation using algebraic operations.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points?

Back

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

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept of a line?

Back

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

Front

How do you write the equation of a line given a point and a slope?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the relationship between parallel lines and their slopes?

Back

Parallel lines have the same slope but different y-intercepts.

Front

What is the relationship between perpendicular lines and their slopes?

Back

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

Front

How do you convert from standard form to slope-intercept form?

Back

To convert, solve for y in terms of x: y = mx + b.