# How do you complete a table for the rule y=3x+2, then plot and connect the points on graph paper?

Aug 6, 2018

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#### Explanation:

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Given:

A linear equation: color(red)(y=f(x)=3x+2

Note that the parent function is color(blue)(y=f(x)=x

color(green)("Step 1"

Consider the parent function and create a data table followed by a graph to understand the behavior of a linear graph.

color(red)(y=f(x)=3x+2

compares with the parent function

color(blue)(y=f(x)=x

Graph of the parent function:

Note that some of the points from the data table are plotted on the graph.

color(green)("Step 2"

Now, we will consider the data table for the function given:

color(red)(y=f(x)=3x+2

From the second table (on the right) above, we will collect just the color(red)((x,y) columns to plot the graph:

Plot and connect the points to create the graph:

color(green)("Step 3"

Let us view both the graphs together and explain transformation.

Observe that the given linear function is in Slope-Intercept Form:

color(red)(y=mx+b

color(red)(m is the Slope.

color(red)(b is the y-intercept.

In our problem, color(blue)(m=3 and b=2

If $\text{Slope > 0}$, 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.