Graphing Linear Equations: When Y = 2/3 XI am trying to figure out how this graph made sense if the coordinates never lined up properly. My numbers were for x,y (0,0) (3,2) (6,3) and somehow I got it right on the practice test even though I guessed on the graph part. I am writing to you without the completed graph because the system would not allow me to post pictures or images.Can I have some feedback with a graph on this please?Shawn Williams

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.1: The Graphing Method
Problem 18WE
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Graphing Linear Equations: When Y = 2/3 X
I am trying to figure out how this graph made sense if the coordinates never lined up properly. My numbers were for x,y (0,0) (3,2) (6,3) and somehow I got it right on the practice test even though I guessed on the graph part. I am writing to you without the completed graph because the system would not allow me to post pictures or images.

Can I have some feedback with a graph on this please?
Shawn Williams

Expert Solution
Step 1

For  a line to pass through three given points, the points need to be collinear.

To check if points are collinear, the slopes of the lines joining them may be checked.

Let A(0,0), B(3,2), C(6,3)

The slopes are given by:

Since the slopes are not equal, the points are not collinear and no line shall pass through all the three points.

So the line y=2/3 x doesn\'t pass through all the three points.

Algebra homework question answer, Step 1, Image 1
Step 2

To check the points lying on the given equation of the line, plugging x=0,3,6 in the equation:

Hence the points lying on the graph of the equation y=2/3 x are (0,0),(3,2) and (6,4)

It can also be seen in the graph.

Algebra homework question answer, Step 2, Image 1
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