Exercise 20 Page 166

When lines are parallel they have the same slope. With this, we know that all lines that are parallel to our given line will have a slope of 13. y=1/3x+10 If we write the desired equation in slope-intercept form, y=mx+b, we can add this slope. y=1/3x+ b To determine the value of b, we can use the fact that our line must pass through point (3,-1). Let's substitute x= 3 and y= -1 into the equation and solve for b.

y=1/3x+b

SubstituteII

x= 3, y= -1

-1=1/3( 3)+b

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Solve for b

FracMultDenomToNumber

a/3* 3 = a

-1=1+b

SubEqn

LHS-1=RHS-1

- 2=b

RearrangeEqn

Rearrange equation

b= -2

Now that we have the y-intercept, we can write the equation of the line parallel to y= 13+10 that passes through (3,-1). y=1/3x+( -2) ⇔ y=1/3x-2