Question

A liner is parallel to y = 3x-13 and intersects the point (1,-2) . What is the equation of this parallel line ?

Answer 1

y=3x-5

Explanation:

Use the point slope formula:

`y-y_(1) =m(x-x_(1))`

Slope (m)

We know the slope is 3, because parallel lines have the same slopes.

y = 3x-13

This is in y=mx+b form, where m is the slope and b is the y intercept. We know that 3 is the slope because it is being multiplied by x.

Point (x1, y1)

Points are written like so: (x, y)

So, for (1, -2), 1 is our x1, and -2 is our y1.

Now we know the m is 3, x1 is 1 and y1 is -2, so we can substitute them in

`y-y_(1) =m(x-x_(1))`

y- -2=3(x-1)

y+2=3(x-1)

y+2= 3*x + 3*-1 Distribute the 3

y+2=3x-3

y+2-2=3x-3-3 Subtract 2 from both sides

y=3x-5

Answer 2

y = 3x - 5

Explanation:

If a line is parallel to another line, the slopes are the same. This means that the equation we will find is y = 3x + b, where b is real.

Plug in point

-2 = 3(1) + b

Simplify

-2 = 3 + b

Simplify

-5 = b

y = 3x -5