Exercise 11 Page 243

When lines are parallel, they have the same slope. Let's rewrite the given equation to clearly see the slope. y=x+4 ⇔ y=1x+4 The slope of the line represented by the above equation is 1. Therefore, the slope of any parallel line will also be 1. y=1x+b ⇔ y=x+b To find the equation of a parallel line through the point ( 3, -2), we will substitute 3 and - 2 for x and y respectively, in the above formula.

y=x+b

SubstituteII

x= 3, y= -2

-2= 3+b

SubEqn

LHS-3=RHS-3

- 5=b

RearrangeEqn

Rearrange equation

b=- 5

Now that we know the y-intercept is - 5, we can write the equation of the parallel line through the given point. y=x+( - 5) ⇔ y=x-5