Topic 4 understanding linear relationships

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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 = 0.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as x increases, y also increases.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as x increases, y decreases.

Front

What is a proportional relationship?

Back

A proportional relationship is one where the ratio of y to x is constant, meaning it passes through the origin (0,0).

Front

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

Back

If the ratio of every x,y coordinate in the table is equivalent, the relationship is proportional.

Front

What does the slope represent in a real-world context, such as cost per item?

Back

The slope represents the rate of change, such as the increase in cost for each additional item purchased.

Front

What is the significance of the y-intercept in a real-world scenario?

Back

The y-intercept can represent a starting value, such as initial cost or quantity before any changes occur.