Writing Equations of Parallel Lines

Parallel lines have the same slope. Let's start by considering the given line.

y = 5 x - 2

We see that the slope is

5 .

Therefore, all parallel lines to the given one will have a slope of

5 .

Let's write a partial equation of these lines in slope-intercept form.

y = 5 x + b

Finally, we are told that the line whose equation we are asked to write passes through the origin. To find its

y -

intercept

b,

we will substitute

0

for

x

and

y .

y = 5 x + b

SubstituteII

x = 0

,

y = 0

0 = 5 \cdot 0 + b

Solve for

b

MultiplyMultiply

0 = 0 + b

AddTermsAdd terms

0 = b

RearrangeEqnRearrange equation

b = 0

Now that we know that

b = 0,

we can write the equation of the parallel line to

y = 5 x - 2

through the origin.

y = 5 x + b \Leftrightarrow y = 5 x

Alternative Solution

Another way of finding the

y -

intercept

If the lines are parallel, then they have the same slope. We can write a partial equation of our line. $y = 5 x + b$ Since we are told the line passes through the origin, we know its $y -$ intercept is $b = 0 .$ $y = 5 x + 0 \Leftrightarrow y = 5 x$

Writing Equations of Parallel Lines 1.3 - Solution

Alternative Solution