venmic wrote:

The line 3x + 4y = 8 passes through all of the quadrants in the coordinate plane except:

A. I

B. II

C. III

D. IV

E. II and IV.

This is a line which doesn't pass through the origin. We know because there is a free term (which doesn't contain neither

x, nor

y).

In this case, we can use the intercept form of the line equation: divide through the equation by the free term 8. We get:

\frac{3x}{8}+\frac{4y}{8}=1 or

\frac{x}{8/3}+\frac{y}{8/2}=1, and finally

\frac{x}{2\frac{2}{3}}+\frac{y}{2}=1.

Now, we can easily see that the

x intercept is

2\frac{2}{3} and the

y intercept is

2.So, our line passes through the points

(2\frac{2}{3},0) and

(0,2). Sketch the line through these two points.

It is a decreasing line which doesn't pass through the third quadrant.

Answer C.

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PhD in Applied Mathematics

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