Slope and Lines Retake

Front

What is the definition of slope in mathematics?

Back

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

Front

What does it mean for a relationship to be proportional?

Back

A proportional relationship is one where two quantities maintain a constant ratio, meaning that as one quantity increases or decreases, the other does so in a consistent manner. The graph of a proportional relationship is a straight line that passes through the origin.

Front

How can you determine if a table of values represents a proportional relationship?

Back

To determine if a table is proportional, check if the ratio of y to x is constant for all pairs of values. If the ratio changes, the relationship is non-proportional.

Front

What is the slope of a line that rises 4 units for every 2 units it runs?

Back

The slope is 2, calculated as rise/run = 4/2.

Front

What does it indicate if a graph does not pass through the origin?

Back

If a graph does not pass through the origin, it indicates that the relationship is non-proportional.

Front

What is the slope of a line represented by the equation y = -3x + 5?

Back

The slope is -3, which is the coefficient of x in the equation.

Front

What is the formula for calculating slope between two points (x1, y1) and (x2, y2)?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does a slope of 0 indicate about a line?

Back

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

Front

What does a negative slope indicate about the direction of a line?

Back

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

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 is 0.