how do u graph this problem y=1/3x+1

Question

how do you graph this linear equation y=1/3x+1

Answer 1

There is a much simpler way to do this. This is a linear (straight-line) equation of the form y=mx+b, with m=1/3, and b=1. These two numbers, m and b, are called the slope and y-intercept of the graph, respectively.

The y-intercept tells you where the graph hits the y-axis. So since b=1, it means the point (0,1) is on the graph. You want to start by drawing that point.

 

The slope tells you how much more the graph will go up for every step to the right. The slope in this case is m=1/3. So the next step is (1, 1+1/3), then after that you have (2, 1+2/3) and (3, 2), (4, 2+1/3) and so on forever. The line goes in the same direction even if x is negative, so some other sample points on the graph are (-1, 2/3), and (-3,0).

We can do another problem to illustrate the point. I just made up the equation y=3x-5. The graph of this one has m=3 and b=-5. That means it starts at (0,-5) and increases by 3 for every step to the right. So other points on the same line would be (1,-2), (2,1),(10,25), (-4,-17), etc. You just have to start at the intercept and add the right amount for each new step in the x-direction.

Ralph's answer is great, by the way, I just thought you might understand better if someone explained what the slope and the y-intercept mean, as well as how to graph this one equation.

Answer 2

William,

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To graph this linear equation, I would set up an x,y table first.  Remember that y is the dependent variable; it's value is determined by what happens to x, the independent variable.  In this instance, x (alone) is being divided by 3 (i.e., 1/3x) then 1 is added to that value.

 

______y__|___1/3x +1___X_________

      .333    | 1/3(-2) + 1  | -2                                                     o

      .67      | 1/3(-1) + 1  | -1                                                   o         The y-intercept = 1.  That when

        1       | 1/3 (0)  +1  | 0                                                   o           x = 0.  Note:  Graph doesn't go

      1.333  |1/3(1)+1      |  1                                                 o             through origin (0,0)

      1.67    | 1/3( 2) +1   |  2                                               o

                |                   |                      This graph is steeper than actual graph but you get the point.

Answer 3

y = (1/3)x + 1

 

 

 

let's use points x =0, and x = 3 and

place these values in the table below:

 

 

x  |  y

--------

0  | 1

3  | 2

 

place these points on a graph paper and draw a line passing through these points. Make sure you draw two arrows from both ends of the line to show that the line has no end.