PreAP: Unit 3 Equations from tables, graphs, word problems

Front

What is the definition of slope in a linear equation?

Back

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

Front

How do you find the slope from a graph?

Back

To find the slope from a graph, select two points on the line, determine the vertical change (rise) and the horizontal change (run) between these points, and then divide the rise by the run.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as 'b' in the equation of a line (y = mx + b). It indicates the value of y when x is 0.

Front

How can you identify the slope and y-intercept from an equation?

Back

In the slope-intercept form of a linear equation (y = mx + b), 'm' represents the slope and 'b' represents the y-intercept.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

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

Front

How do you calculate 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 significance of the slope in real-world applications?

Back

The slope can represent rates of change in real-world contexts, such as speed (distance over time) or cost per item.

Front

How do you interpret the slope in the context of a word problem?

Back

In a word problem, the slope represents the rate of change or relationship between two quantities, such as cost per item or speed.

Front

What is the relationship between slope and parallel lines?

Back

Parallel lines have the same slope, meaning they rise and run at the same rate and will never intersect.