### Video Transcript

Which line graphs the function two π₯ plus three?

Letβs solve this problem by elimination.

Our function is π¦ equals two π₯ plus three. Here is our π₯-axis, and here is our π¦-axis. Our π₯-axis will represent our input value, the value that we put into the equation, and our π¦-axis will be the output of our function.

Now weβre gonna make a table to see some of the sample input and outputs for the function two π₯ plus three. Letβs start with zero. What does π¦ equal if our π₯ has a value of zero? It equals two times zero plus three. Simplified, when π₯ is zero, π¦ equals three.

When π₯ is one, what would π¦ be? π¦ would be equal to five; two times one is two plus three equals five. Now Iβm gonna solve for π₯ equals 20.

Why would we solve for π₯ equals 20? Because our graph is counting by twenties; it will be very easy to see what the π¦ is if π₯ equals 20. Itβs an easily recognizable point on this graph. When π₯ equals 20, π¦ equals 43; 20 times two plus three equals 43.

Now that we have at least three points to check, weβll start comparing the π₯ and the π¦ from our function table to what is represented in the graph. Many times I would recommend starting with zero; looking at zero on the π₯ axis and trying to find the π¦ that corresponds. But because our graph has four lines that are all intersecting pretty close to the same point at zero, letβs check another point.

Letβs check π₯ equals 20, π¦ equals 43 π₯ equals 20; π¦ equals 43 only. One of the lines has an intersecting point at 20, 43. Line π΅ is the correct answer here.

If you wanna confirm this, you can try to solve for π₯ equal 40. In this case, π¦ would equal 83. That point again is found on line π΅, confirming that the line that graphs the function two π₯ plus three is line π΅.