Which of the following statements best describes the graph of 3x - 2y = 4?
a)It is a straight line joining the points (6, 2), (5, 1), and (7, 3).
b) It is a straight line joining the points (0, -2), (2, 1), and (-2, -5).
c) It is a curve joining the points (3, -2), (2, 3), and (4, 1).
d) It is a curve joining the points (0, 2), (-2, -1), and (4, 1).

Solution:

Given,

The equation 3x - 2y = 4.

This is actually in the form of ax + by = c.

Let's see if it satisfies a)

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

3x - 2y = 4.

3(6) - 2(2) = 4.

18 - 4 = 4

This is false, so (6, 2) is not a given line.

Moving to b)

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

3x - 2y = 4.

3(2) - 2(1) = 4.

6 - 2 = 4

This is true, so (2, 1) is on a given line.

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

3x - 2y = 4.

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

0 + 4 = 4

This is true, so (0, -2) is on a given line.

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

3x - 2y = 4.

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

-6 + 10 = 4

4 = 4.

This is true, so (-2, -5) is on a given line.

Therefore, it is a straight line joining the points (0, -2), (2, 1), and (-2, -5).

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

Summary:

The statement which best describes the graph of 3x - 2y = 4 is it is a straight line joining the points (0, -2), (2, 1), and (-2, -5).