Representations of Linear Functions

Front

What is the slope in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept (b) is the value of y when x = 0, indicating where the line crosses the y-axis.

Front

How do you identify the slope from the equation y = 1/2x + 5?

Back

The slope is 1/2, indicating that for every 1 unit increase in x, y increases by 1/2.

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

If the slope is negative, what does that indicate about the line?

Back

A negative slope indicates that the line descends from left to right.

Front

What is the equation of a line with a slope of -2 and a y-intercept of 5?

Back

The equation is y = -2x + 5.

Front

How do you convert a table of values into a linear equation?

Back

Identify the slope (change in y/change in x) and the y-intercept from the table.

Front

What does the equation y = 12x + 35 represent in a real-world context?

Back

It represents a total cost where $35 is a fixed fee and $12 is a variable cost per month.

Front

How can you determine the slope from a graph?

Back

The slope can be determined by selecting two points on the line and calculating the rise over run.

Front

What is the significance of the coefficients in the equation y = 3x + 9?

Back

The coefficient 3 is the slope, and 9 is the y-intercept.