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

1 Answer
Aug 6, 2018

Answer:

#" "#
Please read the explanation.

Explanation:

#" "#
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#

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Graph of the parent function:

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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#

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

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Plot and connect the points to create the graph:

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#color(green)("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:

#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 #"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.