Exercise 98 Page 617

Consider the given equation of a line.

3 x + 2 y = 10

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 = m x + b,

where

m

is the slope and

(0, b)

is the

y -

intercept.

3 x + 2 y = 10

▼

Solve for

y

SubEqn

$LHS - 3 x = RHS - 3 x$

2 y = - 3 x + 10

DivEqn

$LHS / 2 = RHS / 2$

y = \frac{- 3 x + 1 0}{2}

WriteSumFrac

Write as a sum of fractions

y = \frac{- 3 x}{2} + \frac{1 0}{2}

CalcQuot

Calculate quotient

y = \frac{- 3 x}{2} + 5

MoveNegNumToFrac

Put minus sign in front of fraction

y = - \frac{3 x}{2} + 5

MovePartNumRight

$\frac{a \cdot b}{c} = \frac{a}{c} \cdot b$

y = - \frac{3}{2} x + 5

With this information we can more easily identify the slope

m

and

y -

intercept

b .

y = - \frac{3}{2} x + 5

We can write a general equation in slope-intercept form for these lines.

y = - \frac{3}{2} x + b

We are asked to write the equation of a line parallel to the one with given equation that passes through the point

(4, - 7) .

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 = - \frac{3}{2} x + b

SubstituteII

$x = 4$ , $y = - 7$

- 7 = - \frac{3}{2} (4) + b

▼

Solve for

b

MoveRightFacToNum

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

- 7 = - \frac{1 2}{2} + b

CalcQuot

Calculate quotient

- 7 = - 6 + b

AddEqn

$LHS + 6 = RHS + 6$

- 1 = b

RearrangeEqn

Rearrange equation

b = - 1

Now that we have the

y -

intercept, we can write the parallel line to

y = - \frac{3}{2} x + 5

through

(4, - 7) .

y = - \frac{3}{2} x + (- 1) \Leftrightarrow y = - \frac{3}{2} x - 1

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