Search 72,544 tutors
FIND TUTORS
Ask a question
1 0

how do you write an equation with just a graph?

Tutors, please sign in to answer this question.

5 Answers

     Without seeing the graph, I can't help you get the exact answer, but I can give you some tips that might help you.

1.  Since you stated that the graph is a diagonal line, I know that you are looking for a linear equation.  Linear equations can be written in the from y = mx + b.

To get the exact equation, we need to find the values of m and b (you will keep th1.e y and x in the final answer).

2.  The sign on the m value (slope of the line) is determined on whether it goes up or down as you go to the right.  If the line goes up to the right, m is positive.  If the line goes down to the right, m is negative.

3.  Assuming you can see the x and y-axis with hash marks (bold vertical and horizontal lines with small marks evenly spaced along them), you can find the vlaue of m (the slope of the line).  The slope is found by counting how much the line moves up or down through a distance moving right to left.

For example, you might find that at one point of the line you are one mark above the x-axis and two marks right of the y-axis.  Moving along the line, you may find that you are four marks above the x-axis and four marks above the y-axis.  The slope is found by comparing the change in height (1 mark up goes to 4 marks up) and the change in length (2 marks goes up to 4 marks).  The ratio is 3 (4-1) to 2 (4-2), so the slope (m) is 3/2.

4.  If you can see the where the line crosses the y-axis (bold vertical line), you have your b value.

5. If you can't see where the line crosses the y-axis, you can still find the value of b.  Just find a point on the line.  Plug the x and y values of the point, along with the slope (m) into the slope intercept formula (y=mx+b) and solve for b.

6.  Write the slope intercept form of the equation with the values that you found for m and b.

     One other quick tip:  If you have hashes on your x-axis and y-axis, but there are no numbers written, assume that each hash represents 1.

 

To simplify what has already been said, the easiest way to find the equation of a line is to look for the x and y intercepts. One point will be (a, 0) and the other will be (0, b), where a and b are numerical values. The slope is simply m = b/a. When you have the y-intercept, (0, b), you can use the form y = mx + b to find the equation for the line. Consequently with the notation used, you can represent this as y=(b/a)x + b where b is the value from (0,b) and a is the value from (a,0).

Simply just find coordinates of 2 points , and from that you calculate slope:
 
   (x1, y1) , ( x2, y2)    m= (Y1- y2)/ ( x1- x2)
 
      then take y = mx +b
 
           y1= mX1 + b 
 
            then b = y1-mx1 ,you have the equation.
         Intercept points are easy to use, because 1 coordinate point is always 0.
        but , sometimes, they are not an integer, and can not be read accurately from scale, in which case it should take 2 points which have coordinate as integer. 

It sounds like you are saying the diagonal line cuts right through the x-y axis at the origin (or zero point where the x and y axes meet).  If so then my answer would be this.  There are certain graphs that are basice or common and therefore you can know their equation without knowing anything else about them besided their graph.

A line cut through the origin at a diagnal, lets say starting in the positive x and y quadrant (I) and going into the negative x and y quadrant (III) is the graph of y=x.   It is assumed the slope is m=1 and since the line intersects y at y=0 the general equation of a line (y=mx + b) can be simplified to y = x.

Another example would be the "U-shaped" graph that sits at the center of the x-y axis.  Half the "U" is on quadrant I and the other half on the positive y and negative x quadrant (II).  That is the graph of the basic equation of a parobala y = x^2.  If it was the mirror image (or upside down "U") it would be y = -x^2.

To summarize knowing that the graph is centered at the origin and knowing the general equations of lines, parobalas, circles, etc you can usually deduce the equation without any other information.

You should be able to find it using the slope-intercept form:   y = mx + b   , where m is the slope of the line and b represents the y-intercept.

To find the slope, m, pick 2 points on the graph (x, y1) and (x2 , y2) and use the following formula:

     m = (y2 - y1) / (x2 - x1

The y-intercept, b, is the point on the graph where x=0. To find it, look for where the line intersects with the y-axis (this is where x=0).

For example, let say where are looking to find the equation of a graph of a line which has the two points (3, 1) and (0, 7). We want to use the slope-intercept form, y = mx + b ...

    Slope:   m = (7 - 1) / (0 - 3) = (6) / (-3) = -2 ,   thus m = -2

Since the point (0, 7) is a the point where x=0, then we know the y-intercept is at this point. Thus, b = 7.

Therefore, the equation of this line looks like the following:

    y = mx + b     ===>     y = -2x + 7