Question

Which of the following statements best describes the graph of 3x – 2y = 4?

Answer 1

Answer:

B

Step-by-step explanation:

This is actually in the form of ax+by=c which is called standard form for a line.

I also know it is linear because the degree is 1.  I know the degree is 1 because both variables are to the first power (you don't see this number because $x^1=x$ or $y^1=y$).

So the choices are between A and B.

Let's see if it satisfies A:

Checking (6,2) for (x,y):

3 x - 2 y=4

3(6)-2(2)=4

18  -   4  =4

     14    =4 is false so (6,2) is not on the given line.

Moving on to B:

Checking (0,-2) for (x,y):

3 x - 2 y=4

3(0)-2(-2)=4

0   +  4   =4

         4    =4 is true so (0,-2) is on the given line.

Checking (2,1) for (x,y):

3 x - 2 y=4

3(2)-2(1)=4

6  -  2  =4

      4    =4 is true so (2,1) is on the given line.

Checking (-2,-5) for (x,y):

3 x - 2 y=4

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

-6   +  10  =4

           4  =4 is true so (-2,-5) is on the given line.

We have that all three pairs from choice B are contained on the line given.

Answer 2

Answer:

B).

Step-by-step explanation:

3x - 2y = 4 contains variables of degree one only, so this is a straight line.

Convert to slope-intercept form so it will be easier to check:

3x - 2y = 4  

-2y = -3x + 4

y = 3/2 x - 2.

A).  (6, 2): y = 3/2 *6 - 2 = 9-2 = 7 so its not A.

B). (0, -2): y = 0 - 2 = -2 so this fits.

(2, 1): y = 3/2 * 2 - 2 = 1 so this fits.

(-2, -5):  y = 3/2*(-2) - 2 - -3-2 = -5 so this fits.