Exercise 30 Page 594

Recall that parallel lines have the same slope.

We can see that the slope of the given line is 2. Because of this, we know that all lines that are parallel to the given line will have a slope of 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 given one that passes through the point ( 1, 3). 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= 1, y= 3

3=2( 1)+b

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Solve for b

MultByOne

a * 1=a

3=2+b

SubEqn

LHS-2=RHS-2

1=b

RearrangeEqn

Rearrange equation

b=1

Now that we have the y-intercept, we can write the equation. y=2x+ 1 This corresponds to option A.