# parallel line to y = -2x + 2 through the point (5, 3)

#### tryjac

##### New member
Could I get some help with the following:

Write an equation of the line that goes through the point (5, 3) and is parallel to the line y = -2x + 2

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: parallel line through a point

tryjac said:
Could I get some help with
Write an equation of the line that goes through the point (5,3) and is parallel to the line y= -2x + 2
If a line with slope "m" goes through a point $$\displaystyle (x_1, y_1)$$, then the equation of the line is:

$$\displaystyle y\, = \, m\cdot x + (y_1 \, - \, m\cdot x_1)$$

#### nycfunction

##### New member
tryjac said:
Could I get some help with the following:

Write an equation of the line that goes through the point (5, 3) and is parallel to the line y = -2x + 2
You need to use the point-slope formula.

y - y1 = m(x - x1), where (x1, y1) represents the point you were given or point (5, 3).

Since the equation of the line we seek is parallel to the given equation in the question, then the slope must be the same. So, our slope is -2.

We now plug and chug.

y - 5 = -2(x - 3)

y - 5 = -2x + 6

We now isolate y.

y = -2x + 6 + 5

y = -2x + 11....This equation is parallel to the the equation given to you in the question.
How do I know it's parallel? The slope is -2 for BOTH equations.

That's it!