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

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Answer 1 · 2018-08-06T17:36:13

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Please read the explanation.

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Given:

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

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

$Step 1$ $color(green)("Step 1"$

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

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

compares with the parent function

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

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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.

$Step 2$ $color(green)("Step 2"$

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

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

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

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Plot and connect the points to create the graph:

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$Step 3$ $color(green)("Step 3"$

Let us view both the graphs together and explain transformation.

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

$y = m x + b$ $color(red)(y=mx+b$

$m$ $color(red)(m$ is the Slope.

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

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

If $Slope > 0$ $"Slope > 0"$ , as is in our problem, the Slope is positive and the line increases from left to right.

If $b > 0$ $b>0$ , like in our problem, there is a vertical shift up $b$ $b$ units.

Since $b = 2$ $b=2$ , the vertical shift is up 2 units.

Hope this helps.