Exercise 12 Page 243

When lines are parallel, they have the same slope. Let's consider the given equation. y=3x-5 The slope of the line represented by the above equation is 3. Therefore, the slope of any parallel line will also be 3. y=3x+b To find the equation of a parallel line through the point 4, -3, we will substitute 4 and - 3 for x and y respectively, in the above formula.

y=3x+b

SubstituteII

x= 4, y= -3

-3=3( 4)+b

Multiply

Multiply

- 3=12+b

SubEqn

LHS-12=RHS-12

- 15=b

RearrangeEqn

Rearrange equation

b=- 15

Now that we know the y-intercept is - 15, we can write the equation of the parallel line through the given point. y=3x+( - 15) ⇔ y=3x-15