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].
