Intro to Rates: Slope from Table, Graph, Equation

Front

What is the definition of slope in the context of a linear equation?

Back

The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). 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 from a linear equation in the form y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope. Therefore, the slope can be directly identified as the coefficient of x.

Front

What is the slope of the line represented by the equation y = 3x + 1?

Back

The slope of the line is 3.

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 slope of the line that passes through the points (2, 3) and (4, 6)?

Back

The slope is (6 - 3) / (4 - 2) = 3 / 2.

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

What is the slope of the line represented by the equation y = -1/2x + 4?

Back

The slope of the line is -1/2.

Front

What is the slope of the line represented by the equation y = 1/4x - 2?

Back

The slope of the line is 1/4.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in y as x changes.