Writing Equations from tables

Front

What is the y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis. In the equation y = mx + b, it is represented by 'b'. For example, in the equation y = -2x + 5, the y-intercept is 5.

Front

How do you determine the slope from a table of values?

Back

The slope (m) is calculated as the change in y divided by the change in x (m = Δy/Δx). For example, if the table shows points (1, 2) and (2, 5), the slope is (5-2)/(2-1) = 3.

Front

What is the equation for a linear relationship?

Back

A linear relationship can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify the slope from a graph?

Back

The slope can be identified by selecting two points on the line, calculating the rise (change in y) and run (change in x), and then using the formula m = rise/run.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, showing an inverse relationship between the two variables.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, showing a direct relationship between the two variables.

Front

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

Back

The y-intercept can represent the starting value of a dependent variable when the independent variable is zero. For example, in a cost equation, it may represent fixed costs.

Front

How can you write an equation from a table of values?

Back

To write an equation from a table, identify the slope using two points, find the y-intercept, and then use the slope-intercept form y = mx + b.

Front

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

Back

The slope of the line is 3, which means for every unit increase in x, y increases by 3.

Front

What is the y-intercept of the equation y = -4x + 1?

Back

The y-intercept is 1, meaning the line crosses the y-axis at the point (0, 1).