Determine the graph of a linear function showing its intercepts

Question

Graph the function f(x)= 2x+4

Answer 1

The intercepts of f(x) = 2x + 4 can be found by plugging in 0 for x and solving for y to find the y-intercept.  Conversely, plugging in 0 for y and solving for x will give you the x-intercept.  Let's start with the x-intercept:

 

y = 2x + 4

0 = 2x + 4

-4 = 2x

-2 = x

 

The x-intercept is (-2,0).

 

To find the y-intercept:

 

y = 2x + 4

y = 2(0) + 4

y = 4

 

The y-intercept is (0,4).

 

You can also determine the y-intercept quickly because the function is in slope-intercept form (i.e., y = mx + b), where b is the y-intercept (4).

 

To graph the line, you can plot each intercept and then connect them to form a line.  Alternatively, you can plot one intercept, then use the slope (m = 2) to draw the line.  In this case, the slope of 2 means that you move 2 units up and 1 unit to the right (slope = rise/run).