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A linear function F models a relationship in which the dependent variable decreases 6 units for every 3 units the independent variable decreases. The value of the function at 0 is 4. Graph the function. Identify the slope, y-intercept, and x-intercept of the graph.

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A. Finding the slope

The slope of the function is simply the ratio of the value of the dependent variable over the independent variable, so in this case it is:

slope = 6/ 3 = 2

 

B. Finding the y – intercept

The y – intercept is simply the value of the dependent variable when the independent variable is equal to zero, therefore:

y – intercept (b) = 4

 

C. Finding the function of the graph

The general equation of a line is given as:

y = m x + b

where m is the slope and b is the y intercept therefore:

y = 2 x + 4

 

D. Finding the x – intercept

The x – intercept is simply the value of the independent variable (x) when the dependent variable (y) is equal to zero, therefore:

0 = 2 x + 4

x = - 2

 

E. Graph the function

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