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

Question

40634 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-08-06T17:36:13

$" "$
Please read the 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

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

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.

$color(green)("Step 2"$

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

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

enter image source here

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

enter image source here

Plot and connect the points to create the graph:

enter image source here

$color(green)("Step 3"$

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.