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

Answer:

D.

Step-by-step explanation:

The equation given takes the point-slope form which is, [tex] y - b = m(x - a) [/tex]. 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 [tex] y - 2 = 3(x - 1) [/tex], look for the points which will give you something almost exactly as the equation if you substitute their values into [tex] y - b = m(x - a) [/tex].

Let's consider option D.

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

Substitute these into [tex] y - b = m(x - a) [/tex]

We have:

[tex] y - (2) = m(x - (1)) [/tex]

[tex] y - 2 = m(x - 1) [/tex]

As you can see, this looks almost exactly as

[tex] y - 2 = 3(x - 1) [/tex].

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 [tex] y - 2 = m(x - 1) [/tex] to find m:

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

[tex] -1 - 2 = m(0 - 1) [/tex]

[tex] -3 = m(-1) [/tex]

[tex] -3 = -m [/tex]

Divide both sides by -1

3 = m

m = 3.

Therefore, option D is the graph of the line [tex] y - 2 = 3(x - 1) [/tex].

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