Exercise 4 Page 662

Consider the given equation of a line. x+1/2y=- 1 When lines are parallel, they have the same slope. Because of this, we know that all lines that are parallel to the line whose equation is given will have a slope of - 2. To help us identify the slope of this line, let's first convert it into slope-intercept form, y= mx+ b, where m is the slope and (0, b) is the y-intercept. With this, we can more easily identify the slope m and y-intercept b. y= - 2x-2 ⇓ y= - 2x+( - 2) We can write a general equation in slope-intercept form for these lines. y= - 2x+ b We are asked to write the equation of a line parallel to the one with given equation that passes through the point ( 2, 5). By substituting this point into the above equation for x and y, we will be able to solve for the y-intercept b of the parallel line.

y=- 2x+b

SubstituteII

x= 2, y= 5

5=- 2( 2)+b

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Solve for b

Multiply

Multiply

5= - 4+b

AddEqn

LHS+4=RHS+4

9=b

RearrangeEqn

Rearrange equation

b=9

Now that we have the y-intercept, we can write the equation of the line parallel to x+ 12y=- 1 that passes through (2,5). y= - 2x+ 9 Therefore, the answer is A.

Checking Our Answer

Graphs of the Lines

We can verify our answer by graphing both lines on the same coordinate plane. If they are parallel, they will never intersect.

We can see by looking at the graphs of the functions that they are indeed parallel.