Question

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

Answer 1

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Please read the explanation.

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 `"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.