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Chapter 11: Q. 2 (page 713)

(a) Graph the line : 3x+4y=12.

(b) What is the slope of a line parallel to this line?

Short Answer

Expert verified

(a) Graph of the line 3x+4y=12is shown below.

(b) The slope of the parallel line is-34or-0.75.

Step by step solution

01

Part (a) Step 1. Given information.

The given equation is:

3x+4y=12

02

Part (a) Step 2. Determine the intercepts.

Substitute x=0 to find y-intercept.

3(0)+4y=124y=12y=124y=3

Substitue y=0 to find the x-intercept.

3x+4(0)=123x=12x=123x=4

So, graph intersect the x-axis at (4,0) and the y-axis at(0,3).

03

Part (a) Step 3. Draw the graph.

Plot the points (0,3)and (4,0)on a coordinate plane and connect them by a straight line.

04

Part (b) Step 1 Given information.

The given equation is:

3x+4y=12

05

Part (b) Step 2. Determine the slope of the parallel line.

The slope of the line ax+by=cis m=-ab.

In the given equation a=3,b=4. So, the slope of the given line is:

m=-34

The slopes of parallel lines are always equal. It means the slope of the parallel is-34or-0.75.

06

Part (b) Step 3. Conclusion.

The slope of the parallel line is-34or-0.75.

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