Exercise 3 Page 211

When lines are parallel, they have the same slope. y= 3x- 1 Because of this, we know that all lines that are parallel to our given line will have a slope of 3. This means we can write a general equation in slope-intercept form for all lines parallel to the given equation. y= 3x+ b We are asked to write the equation of a line parallel to the given equation that passes through the given point ( -2, -8). By substituting this point into the general equation for x and y, we will be able to solve for the y-intercept b of the parallel line.

y=3x+b

SubstituteII

x= -2, y= -8

-8=3( -2)+b

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Solve for b

MultPosNeg

a(- b)=- a * b

-8=-6+b

AddEqn

LHS+6=RHS+6

-2=b

RearrangeEqn

Rearrange equation

b=-2

Now that we have the y-intercept, we can write the equation of the line that is parallel to y=3x-1 and passes through the point (-2,-8). y= 3x+( -2) ⇒ y=3x-2