Question

Some methods for graphing equations work well with certain equations and some don’t. Knowing which method to select based on the given equation is a valuable skill. You have learned three methods to graph equations. These methods are:

y = mx + b
find intercepts
use a t-chart

A. Post your response to the discussion board.

Using the following 3 equations, answer the questions:
11 x plus y equals 4 space x plus y equals negative 2 space x minus 2 y equals 18

How can you determine which equations can be graphed more easily using x- and y-intercepts, rewriting in slope-intercept form, or using a table of values?
Which method works best for you personally? When does it not work as well?

Answer 1

Explanation:

I tried to translate "11 x plus y equals 4 space x plus y equals negative 2 space x minus 2 y equals 18"

This is what I got:

11x + y = 4

x+y=-2

x-2y=18

For me, personally, I need to rewrite these equations into standard format of y=mx+b (slope intercept):

-------

11x + y = 4

y=-11x+4

-------

x+y=-2

y=-x-2

-------

x-2y=18

2y = x-18

y=(1/2)x-9

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For each one I can find the y-intercept easily: (4, -2. and -9). I can quickly generate a second point by assuming a convenient value for x (one that makes the calculation simple).

1. y=-11x+4 let x = 1; y = -7 : (1,-7)

y=-x-2 let x = 2; y= -4 : (2,-4)

y=(1/2)x-9 let x= 2; y=-8 : (2,8)

The y-intercepts tell us at point on the line for each equation:

(4, -2. and -9) means points at (0,4), (0,-2) and (0.-9)

Now we have two point for each line equations. All we have to do is mark those two points for each equation and draw a line through them. Easy!

The two points for each equation are:

1. (1,-7), (0,4)

2. (2,-4), (0,-2)

3. (2,8), (0.-9)

This always works well for equation of lines. More comples equations involving parabolas, etc., are more easily graphed using tables of the results of various x inputs.