Linear Equations Test Review

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

What is the formula for calculating 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 in 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

How do you identify a positive slope on a graph?

Back

A positive slope rises from left to right, indicating that as x increases, y also increases.

Front

How do you identify a negative slope on a graph?

Back

A negative slope falls from left to right, indicating that as x increases, y decreases.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What does it mean if a slope is undefined?

Back

An undefined slope occurs in a vertical line, where the change in x is zero, making the slope calculation (y2 - y1) / (0) impossible.

Front

How do you convert the equation y - 3 = -5(x + 2) to slope-intercept form?

Back

To convert to slope-intercept form, simplify to y = -5x - 10 + 3, which gives y = -5x - 7.

Front

What is the slope of the line represented by the equation -7x + 2y = 9?

Back

To find the slope, rearrange to slope-intercept form: 2y = 7x + 9, so y = (7/2)x + 9/2. The slope is 7/2.