Writing Equations of Parallel Lines

As the lines

L_{1}

and

L_{2}

are parallel, the line

L_{1}

, must have the same slope as

L_{2} .

Therefore, we can start the equation by substituting

m

with

4

in the slope-intercept form.

y = 4 x + b

To find the

y

-intercept,

b,

we'll use the given point

(4, 17)

. Substitute this point's coordinates into the equation

y = 4 x + b

, and then solve for

b .

y = 4 x + b

x = 4

,

y = 17

17 = 4 \cdot 4 + b

Solve for

b

17 = 16 + b

LHS - 16 = RHS - 16

1 = b

RearrangeEqnRearrange equation

b = 1

The line

L_{1}

has the equation

y = 4 x + 1 .

Writing Equations of Parallel Lines 1.6 - Solution