Writing equations of lines

Question

Write an equation that is parallel to 3y=8x, through (-9,2)

Answer 1

Parallel lines have the same slope so you need to determine the slope of the line 3y = 8x

We can write the equation in slope-intercept form first (or y = mx + b) by dividing both sides of

the equation by 3: y = 8 x + 0

3

Therefore the slope of the given line is 8 . This will also be the slope of the new line that is parallel and

3

passes thru (-9,2). y = 8 x + b

3

We can substitute -9 for x and 2 for y to determine the y-intercept or b for the parallel line:

y = 8 x + b

3

2 = 8 * (-9) + b

3

2 = -24 + b

26 = b

So the equation of the line parallel to the given line thru (-9, 2) is y = 8 x + 26

3

Answer 2

First you need to solve it for y so that you can find the slope of this line. Divide both sides by 3 and you'll get y = 8/3x. Now it is slope intercept form y =mx +b. Since the number in front of x is the slope, then the slope of this line is 8/3. Since parallel lines have the same slop, your new lines slope is 8/3. Plug that into y=mx+b, y = 8/3x + b. Now you have to find b. Plug in the point they gave you (-9,2) so x=-9 and y=2. 2=8/3(-9)+b. Now solve for b. So, 2 =-24+b, add 24 to both sides. So, b=26. Now put the slope and y I tercept back in the equation. y =8/3x +26. That's it!