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Chapter 3: Q 3.59. (page 286)

Find an equation of a line parallel to the line y=3x+1that contains the point (4,2). Write the equation in slope-intercept form.

Short Answer

Expert verified

The equation isy=3x-10.

Step by step solution

01

Step 1. Find the slope of the given line

The given line is y=3x+1.

The line is already in the slope-intercepted form.

Therefore the slope is:

m=3

02

Step 2. Find the slope of the parallel line and identify the point

As we know that parallel lines have the same slope.

Therefore the slope of the parallel line is:

m1=3

The given point is (4,2).

(x1,y1)=(4,2)

03

Step 3. Substitute the values into the point-slope form 

The point-slope form is:

y-y1=m(x-x1)

role="math" localid="1644432036292" y-2=3(x-4)y-2=3x-12

04

Step 4. Write the equation in slope-intercept form

The slope-intercept form of the equation isy=3x-10.

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