Linear Equations Review

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, represented as the ratio of the vertical change to the horizontal change between two points on the line.

Front

How do you identify the slope from a graph?

Back

The slope can be identified by selecting two points on the line and calculating the rise (change in y) over the run (change in x).

Front

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

Back

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

Front

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

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 can you determine the y-intercept from a graph?

Back

The y-intercept can be determined by locating the point where the line intersects the y-axis.

Front

What is the relationship between the slope and the direction of a line?

Back

A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right.

Front

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

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What is the significance of a slope of zero?

Back

A slope of zero indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where x remains constant while y changes.

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).