Exercise 1 Page 242

Consider the given equation of a line. y= 1/2x-3 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 12. We can write a general equation in slope-intercept form for these lines. y= 1/2x+ b We are asked to write the equation of a line parallel to the given equation that passes through the point ( - 1, 2). 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=1/2x+b

SubstituteII

x= - 1, y= 2

2=1/2( - 1)+b

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Solve for b

MoveRightFacToNumOne

1/b* a = a/b

2=- 1/2+b

MoveNegNumToFrac

Put minus sign in front of fraction

2=- 1/2+b

AddEqn

LHS+1/2=RHS+1/2

2+1/2=b

NumberToFrac

a = 2* a/2

4/2+1/2=b

AddFrac

Add fractions

5/2=b

RearrangeEqn

Rearrange equation

b=5/2

Now that we have the y-intercept, we can write the parallel line to y= 12x-3 through (- 1,2). y= 1/2x+ 5/2

Checking Our Answer

Check By Graphing

Finally, 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.