Question

Which is the graph of the line LaTeX: y-2=3\left(x-1\right)y − 2 = 3 ( x − 1 )?

Answer 1

D.

Explanation:

The equation given takes the point-slope form which is,
`y - b = m(x - a)`. Where,

(a, b) = (x, y) coordinates of a point on the line.

m = slope of the line .

To find which graph has a line equation of
`y - 2 = 3(x - 1)`, look for the points which will give you something almost exactly as the equation if you substitute their values into
`y - b = m(x - a)`.

Let's consider option D.

We have a given point (1, 2). a = 1, b = 2.

Substitute these into
`y - b = m(x - a)`

We have:

`y - (2) = m(x - (1))`

`y - 2 = m(x - 1)`

As you can see, this looks almost exactly as

`y - 2 = 3(x - 1)`.

If you want to be certain that option D is the answer, find m by using the coordinates of any other point on the line and plug into
`y - 2 = m(x - 1)` to find m:

In graph D, let's take the points (0, -1)

`-1 - 2 = m(0 - 1)`

`-3 = m(-1)`

`-3 = -m`

Divide both sides by -1

3 = m

m = 3.

Therefore, option D is the graph of the line
`y - 2 = 3(x - 1)`.