Determine the graph of a linear function showing its intercepts

Question

F(X)= -8/3X+8

Answer 1

Let x = 0, then what is y?  (it's 8)

 

Let y = 0, then what is x?

 

This gives you the two intercepts on y and x axes, respectively.

 

This is usually the best way to graph a straight line -- by its intercepts.

Answer 2

The function:    f(x)=-(8/3)x+8
  may be plotted on the Cartesian Coordinate System (x-and-y) with f(x) meaning y.
 
Two points determine a line.  Connect those two points and keep on going in each direction.
 
Often, the y-intercept (the value of y when x=0) and the x-intercept (the value of x when y=0) are easy to find.  Here, those two points are:
     (0,8)         [where line crosses y-axis]
     (3,0)         [where line crosses x-axis]
 
= = = = = = = = = = =
Chris wants to see this worked out step-by-step and WyzAnt Answers may be edited but Comments may not, so I'll respond here.  Also, the Answers Forum does not permit graphics, animation, sound, etc., so this response is really limited.  Chris, send me a message if you are interested in online tutoring sessions.
 
(1) A problem give an equation and asks you to plot the line.
       Note that a line is a function.  That is, y=f(x), so there is, at most one value of y for each allowable value of x.
       So, if the equation is not in the form y=f(x), then first solve for y.
            Ex.   4x + 2y = 7  is in Standard Form
                      y = -2x + 7/2 is the same equation in point-slope form
                                   2y = -4x + 7   (subtract 4x from both sides)
                                    y = -2x + 7/2    (divide both sides by 2)
 
(2) The intercepts (definitions) --
   The y-intercept is the value of y when x=0, the point (0,y), the place where the line crosses the y-axis.
   The x-intercept is the value of x when y=0, the point (x,0), the place where the line crosses the x-axis.
 
(3) Find the y-intercept [so, set x=0 and solve]
        y= -2x + 7/2
        y= -2(0) + 7/2
        y = 7/2
      The y-intercept is (0,7/2).
          From the Origin [the point (0,0], go 0 to the right (so, stay on the y-axis), then go 7/2 up [3 1/2].
 
(4) Find the x-intercept [so, set y=0 and solve]
       y = -2x + 7/2
       0 = -2x + 7/2
       2x = 7/2              [add 2x to both sides]
       x = 7/4      [that is, 1 3/4]
      The y-intercept is (7/4, 0) or (1 3/4, 0).
         From the Origin, stay on the x-axis and go 7/4 [that is, 1 3/4] to the right.
 
(5) Now, "Connect the Dots" and keep on going in both directions.  That's the line.
   
(6) Check:  A line in slope-intercept form [y=mx+b] has slope m and y-intercept b.  Let's check:
          line:        y = -2x + 7/2
          slope = -2 means that it goes down (because of -) two units as it goes right one unit.
        Slope is often called "rise over run" because it is (increase in y)/(increase in x).
             This depends on the problem, but I recognize that:
                     When x=1, y=1 1/2     [the point (2, 3/2) is on the line]
                     When x=2, y=-1/2    [the point (3, -1/2) is on the line]
                          The line has gone down 2 as it went right 1.  Slope = -2.