Solve Which equation in point-slope form, is represented by this graph?

y
−
3
=
1
2
(
x
−
4
)
y−3=
2
1

(x−4)

y
=
2
x
+
4
y=2x+4

y
−
3
=
3
(
x
−
4
)
y−3=3(x−4)

y
−
3
=
1
2
(
x
−
7
)
y−3=
2
1

(x−7)

y - 3 = (1/2)(x - 4)

Step-by-step explanation:

The graph is hard to read, but we can make assumptions about the x- and y-values shown.  The y-intercept appears to be (0, 1) and the blue dot appears to be (4, 3).  Let's try finding the equation of the line using this assumed data:

The point-slope equation is y - k = m(x - h), where (h, k) is a point on the line and m is the slope of the line.

We need the slope of the line.  Recall that m = rise/run.  Going from (0, 1) to (4, 3), x (the 'run') increases by 4 and y (the 'rise') increases by 2.  Thus, the slope is m = rise/run = 2/4, or 1/2.

Substituting the known values into the point-slope equation y - k = m(x - h), we get:

y - 3 = (1/2)(x - 4)