Exercise 2 Page 333

Parallel lines have the same slope. With this in mind, consider the given equation. y= -4x+1 We see that the slope of the above line is -4. Therefore, the slope of any parallel line will have a slope of - 4. Using this information, we can write a general equation in slope-intercept form for any line which is parallel to the given one. y= -4x+b We are asked to write the equation of a parallel line to the given one that passes through the point ( 3, - 1). By substituting 3 and -1 for x and y, respectively, in the above formula, we will be able to find the y-intercept b.

y=-4x+b

SubstituteII

x= 3, y= -1

-1=-4( 3)+b

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Solve for b

MultNegPos

(- a)b = - ab

-1=-12+b

AddEqn

LHS+12=RHS+12

11=b

RearrangeEqn

Rearrange equation

b=11

Now that we know that b=11, we can write the equation of the line that passes through (3, - 1) and is parallel to y=- 4x+1. y=-4x+11