10/28 8th Understanding Slope and Proportionality

Front

What is the definition of slope in a linear relationship?

Back

Slope is a measure of the steepness of a line, calculated as the ratio of the rise (change in y) to the run (change in x).

Front

How do you determine if a relationship is proportional?

Back

A relationship is proportional if it can be represented by a straight line that passes through the origin (0,0) and has a constant slope.

Front

What is the formula for the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

What does the y-intercept represent 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.

Front

What is the slope of a line that passes through the points (1, 2) and (3, 6)?

Back

The slope is 2, calculated as (6 - 2) / (3 - 1).

Front

How can you identify a nonproportional relationship from a graph?

Back

A nonproportional relationship can be identified by a line that does not pass through the origin or has a y-intercept other than zero.

Front

What is the equation of a line with a slope of 4 and a y-intercept of -2?

Back

The equation is y = 4x - 2.

Front

If a line has a slope of -1, what does this indicate about the relationship between x and y?

Back

A slope of -1 indicates that as x increases, y decreases at the same rate.

Front

What is the slope of a line represented by the equation y = 2x + 3?

Back

The slope is 2.

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 rise and run between them, and calculate the slope as rise/run.