Final Exam Prep #2

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b). It is calculated as the rise over run, or the change in y divided by the change in x.

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).

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 convert an equation to slope-intercept form?

Back

To convert an equation to slope-intercept form, solve for y in terms of x. For example, from 5x + 3y = 12, rearrange to get y = -5/3x + 4.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the same as the slope, representing how much y changes for a unit change in x.

Front

What does it mean if a graph is non-linear?

Back

If a graph is non-linear, it means that the rate of change is not constant, and the relationship between x and y cannot be represented by a straight line.

Front

How do you determine the equation of a line from a graph?

Back

To determine the equation of a line from a graph, identify the slope and y-intercept, then use the slope-intercept form (y = mx + b).

Front

What is the significance of the y-intercept in a linear equation?

Back

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

Front

What does the term 'rise' refer to in slope calculations?

Back

'Rise' refers to the vertical change between two points on a line, calculated as the difference in their y-coordinates.