Question

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

Answer 1

Answer:

D.

Step-by-step 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 $y - 2 = 3(x - 1)$.