for example: x+2y=6

How would you make those into coordinates on a graph?

for example: x+2y=6

How would you make those into coordinates on a graph?

Tutors, please sign in to answer this question.

Linear equations are the first step to understanding how graphing works. The default equation which will shortly become permanent in your knowledge of math is: y = mx + b

This equation is the slope-intercept form for straight lines where 'm' represents the slope of the line, and 'b' represents the y-axis intercept (when x = 0, y = b).

Using your example, let's first change the equation to be in the slope-intercept form.

x + 2y = 6 [beginning equation]

2y = -x + 6 [subtracting 'x' from each side]

y = -x/2 + 6/2 [dividing each side by 2]

y = -1/2x + 3 [simplify]

Now the equation is in slope-intercept form. From the equation now, we can tell that the
**slope** (m) is -1/2 and the y-axis **intercept** (b) is 3.

An easy first point is the intercept, so (0,3) could be your first point. From there you can either draw a straight line at a slope of negative 1/2 (which is to say for every 2 points you move right on the x-axis, you'll drop down 1 on the y-axis). Or you can input any value for x and find it's corresponding point on y by solving the equation. Making a table can help with that:

__x__|__y__

0 3

2 2

6 0

*a few examples, but any 'x' value would be fine.

First, solve the given equation for y:

x + 2y = 6

2y = -x + 6

y = (-x + 6)/2

y = (-x/2) + (6/2)

y = (-1/2)x + 3

This form of a linear equation is know as the slope-intercept form.

Slope-intercept form: y = mx + b , where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis, or when x=0).

Thus, for the line of the equation y = (-1/2)x + 3 :

m = slope = Δy/Δx = rise/run = -1/2

b = y-intercept = 3 ==> y = 3 when x = 0 ==> (0, 3)

After plotting the y-intercept, (0, 3), use the slope of the line, -1/2, to plot other points.

That is, form the point (0, 3) go down the y-axis 1 point (since the rise part of the slope is negative) and 2 points to the right (since the run part of the slope is positive) which gives you the next set of points to the right of the y-intercept, that being (2, 2). Conversely, you can go up one point on the y-axis and 2 points to the left which gives you the next set of points to the left of the y-intercept, that being (4, -2).

Another way to do this is to simply pick a few x-values and plug them into the linear equation we found to generate the y-value for each x-value, which would give you a few x,y-coordinates to plot. For instance, for the given equation y = (-1/2)x + 3

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

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

when x = 0, y = (-1/2)(0) + 3 = 0 + 3 = 3 ==> (0, 3)

when x = 2, y = (-1/2)(2) + 3 = -1 + 3 = 2 ==> (2, 2)

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

Jonathan S.

Certified, Experienced Tutor and Teacher – Physics, Math, SATs

New York, NY

4.7
(60 ratings)

Tonia M.

Double-Ivy-League-Educated, PhD tutor passionate about teaching!

New York, NY

5.0
(32 ratings)

Sean B.

Math and SAT tutor for all

New York, NY

5.0
(18 ratings)

## Comments