Writing Equations from Tables, Graphs and Situations

Front

What does it mean for a graph to be proportional?

Back

A graph is proportional if it passes through the origin (0,0) and the ratio of the y-values to the x-values is constant.

Front

What does it mean for a graph to be nonproportional?

Back

A graph is nonproportional if it does not pass through the origin or if the ratio of the y-values to the x-values is not constant.

Front

How do you determine the rate of change from a graph?

Back

The rate of change is determined by calculating the slope of the line, which is the change in y divided by the change in x (rise/run).

Front

What is a y-intercept?

Back

The y-intercept is the point where the graph intersects the y-axis, indicating the value of y when x is zero.

Front

How can you identify if a table of values is proportional?

Back

A table is proportional if the ratio of y to x is constant for all pairs of values.

Front

What is the formula for calculating slope?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What is the significance of a negative slope?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

What does a slope of zero indicate about a line?

Back

A slope of zero indicates a horizontal line, meaning there is no change in y as x changes.

Front

What is the relationship between slope and rate of change?

Back

The slope of a line represents the rate of change between the two variables represented on the axes.

Front

How can you find the slope from a table of values?

Back

To find the slope from a table, select two points (x1, y1) and (x2, y2) and use the slope formula: m = (y2 - y1) / (x2 - x1).