Answer:
A linear equation:
y
=
f
(
x
)
=
3
x
+
2
Note that the parent function is
y
=
f
(
x
)
=
x
Explanation:
Step 1
Consider the parent function and create a data table followed by a graph to understand the behavior of a linear graph.
y
=
f
(
x
)
=
3
x
+
2
compares with the parent function
y
=
f
(
x
)
=
x
enter image source here
Graph of the parent function:
enter image source here
Note that some of the points from the data table are plotted on the graph.
Step 2
Now, we will consider the data table for the function given:
y
=
f
(
x
)
=
3
x
+
2
enter image source here
From the second table (on the right) above, we will collect just the
(
x
,
y
)
columns to plot the graph:
enter image source here
Plot and connect the points to create the graph:
enter image source here
Step 3
Let us view both the graphs together and explain transformation.
enter image source here
Observe that the given linear function is in Slope-Intercept Form:
y
=
m
x
+
b
m
is the Slope.
b
is the y-intercept.
In our problem,
m
=
3
and
b
=
2
If
Slope > 0
, as is in our problem, the Slope is positive and the line increases from left to right.
If
b
>
0
, like in our problem, there is a vertical shift up
b
units.
Since
b
=
2
, the vertical shift is up 2 units.
Hope this helps.