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graph equation 5x-3y=2

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3 Answers

The easiest way to graph the equation 5x - 3y = 2 is to change the equation (from standard form) to the point slope form, y = mx + b, where m = the lines slope and b = the y intercept (where the line crosses the y-axis). Use the following steps to convert the equation's form:

The first step is to isolate the y variable and subtracting 5x from both sides:

5x - 3y = 2         

-5x        -5x

- 3y = - 5x + 2

The next step is to complete the process of isolating y by dividing both sides by -3:

- 3y = - 5x + 2

-3           -3

y = 5/3 x - 2/3

We now have the equation in the slope-intercept form and can graph. Our first point will be the (0, -2/3), or the y-intercept. To find the next point simply use the lines slope (5/3), moving up the y-axis 5 points and then sliding 3 points to the right to the next point (3, 4 1/3).

We can prove this solution by substituting the points back into the original equation:

(0 , -2/3) ---> 5x - 2y = 2

5(0) - 3(-2/3) = 2

2 = 2

(3 , 4 1/3) ---> 5x - 2y = 2

5(3) - 3(4 1/3) = 2

15 - 13 = 2

2 = 2

we 5x-3y = 2. if x= 0 then y = -2/3 and if y=0 then x = 2/5. so we get two points that lie on the line: (0, -2/3) and (2/5,0 ). you now just connect the two points and extend the line in both directions and get the graph of the line you wanted.

Notice that the equation represents a first degree polynomial and, thus, is a linear function. So we first rearrange the equation to have it in slope-intercept form, which looks like the following:

     y = mx + b ,  where m is the slope of the line and b is the y-intercept (y-intercept is the point on the graph where the line intersects with the y-axis, or the point at which x=0).

          5x - 3y = 2

 -5x + 5x - 3y = -5x + 2

               -3y = -5x + 2

        (-3y)/-3 = (-5x + 2)/-3

                  y = (-5x)/-3 + (2)/-3

                  y = (5/3)x - 2/3

Now that the equation of the line is in slope-intercept form, we can plot the y-intercept and use the slope to plot a few more points on the graph.

      y-intercept:   b = -2/3     ==>      plot the point (0, -2/3)

      Slope:         m = 5/3    

To find the next point to the right of (0, -2/3), go 5 points up and 3 points to the right -- this should yield the point (3, 13/3) or (3, 4 1/3). The next point to the right of that would be (6, 9 1/3).

To find the first point to the left of (0, -2/3), go 5 points down and 3 points to the left -- this should yield the point (-3, -17/3) or (-3, -5 2/3). The next point to the left of that would be (-6, -10 2/3).