3-1 to 3-4

Front

What is the slope of a graph that represents the relationship between distance traveled and gallons of gasoline used?

Back

The slope represents the rate of distance traveled per gallon of gasoline used. In this case, the slope is 32.

Front

What is a direct variation?

Back

A direct variation is a relationship between two variables where one variable is a constant multiple of the other, typically expressed in the form y = kx, where k is a non-zero constant.

Front

How can you identify a direct variation graph?

Back

A direct variation graph will be a straight line that passes through the origin (0,0).

Front

What is the general form of the Direct Variation Equation?

Back

The Direct Variation Equation is y = kx, where k is the constant of variation.

Front

If y varies directly with x and y = 14 when x = 6, what is the equation that represents this relationship?

Back

The equation is y = (7/3)x.

Front

What does the constant 'k' represent in the equation y = kx?

Back

The constant 'k' represents the constant of variation, indicating how much y changes for a unit change in x.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction of the relationship between the two variables.

Front

How do you calculate 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 equation of a line with a slope of 1/2?

Back

The equation of the line can be expressed as y = (1/2)x + b, where b is the y-intercept.

Front

What does it mean if a graph has a slope of 0?

Back

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