Questions: Graph the function with the given description. A linear function f models a relationship in which the dependent variable decreases 4 units for every 2 units the independent variable increases, and f(0)=-2.

Graph the function with the given description.

A linear function f models a relationship in which the dependent variable decreases 4 units for every 2 units the independent variable increases, and f(0)=-2.

Transcript text: Graph the function with the given description. A linear function $f$ models a relationship in which the dependent variable decreases 4 units for every 2 units the independent variable increases, and $f(0)=-2$.

Solution

Solution Steps

Step 1: Find the slope

The dependent variable decreases 4 units for every 2 units the independent variable increases. This gives a slope of -4/2 = -2.

Step 2: Find the y-intercept

The problem states that _f_(0) = -2. This means the y-intercept is -2.

Step 3: Write the equation of the line and plot the graph

Using the slope-intercept form, the equation of the line is _y_ = -2_x_ - 2. The graph can be plotted using the y-intercept (0, -2) and the slope -2. Another point can be found by moving 1 unit to the right and 2 units down from the y-intercept, which gives the point (1, -4). Plotting these two points and drawing a line through them yields the graph.