Exercise 9 Page 334

Consider the given equation of a line. y+2=4(x-1) When lines are parallel, they have the same slope. To help us identify the slope of this line, let's first convert it into slope-intercept form, y=mx+ b, where m is the slope and (0, b) is the y-intercept.

y + 2 = 4(x-1)

▼

Solve for y

SubEqn

LHS-2=RHS-2

y = 4(x-1)-2

Distr

Distribute 4

y = 4x - 4 - 2

SubTerm

Subtract term

y=4x - 6

With this, we can more easily identify the slope m. y=4x-6 We can write a general equation in slope-intercept form for these lines. y=4x+ b We are asked to write the equation of a line parallel to the given equation that passes through the point ( 1, - 3). By substituting this point into the above equation for x and y, we will be able to solve for the y-intercept b of the parallel line.

y=4x+b

SubstituteII

x= 1, y= -3

-3=4( 1)+b

▼

Solve for b

Multiply

Multiply

-3=4+b

SubEqn

LHS-4=RHS-4

-7=b

RearrangeEqn

Rearrange equation

b=-7

Now that we have the y-intercept, we can write the parallel line to y+2 = 4(x-1) through (1,- 3). y=4x+( - 7) ⇔ y = 4x - 7