Question Video: Identifying the Line Graph of a Given Function from a Set of Line Graphs Mathematics

Video Transcript

Which line graphs the function two 𝑥 plus three?

Let’s solve this problem by elimination.

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

Now we’re gonna make a table to see some of the sample input and outputs for the function two 𝑥 plus three. Let’s start with zero. What does 𝑦 equal if our 𝑥 has a value of zero? It equals two times zero plus three. Simplified, when 𝑥 is zero, 𝑦 equals three.

When 𝑥 is one, what would 𝑦 be? 𝑦 would be equal to five; two times one is two plus three equals five. Now I’m gonna solve for 𝑥 equals 20.

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

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

Let’s check 𝑥 equals 20, 𝑦 equals 43 𝑥 equals 20; 𝑦 equals 43 only. One of the lines has an intersecting point at 20, 43. Line 𝐵 is the correct answer here.

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