In Exercises 47–50, write each English sentence as an equation in...

Question

In Exercises 47–50, write each English sentence as an equation in two variables. Then graph the equation.

The y-value is the difference between four and twice the x-value.

Accepted Answer

Hey everyone in this problem we are asked to use the following english sentence to write an equation and a graph. Okay. And the sentence we're given is the y value is nine more than five times the x value. Okay, Alright, so let's break this down bit by bit. It starts by saying the y value is when we hear the y value is that means why is equal to Okay, now the next part says nine more. Okay, so that means we're adding nine mm Plus 9. 9 More. Okay, nine more than what? Nine more than five times the X value. Okay, five times the X value is five X. Okay so we have Y is which is Y equals nine more? Okay, so we're adding 9 to 5 times the X value. Five X. Okay and so we see this equation is the equation of a line, Y is equal to five X plus nine. Okay, we have our equation. Let's figure out how to graph this. Well let's look at first what kind of slope we're gonna have. Okay, we see that the coefficient with the X is positive so we have a positive slope. Now let's find our X. And y intercepts. That's gonna help us graph this as well. Can I start with the X intercept, this is when y is zero, so we have zero is equal to five X plus nine which gives us x is equal to negative 9/5. If we want to write this as a decimal, we see decimals kind of in the answers were given. So let's write this as a decimal. This is going to be negative 1.8. And so we get the point negative 1.8 zero. And if we find our y intercept this is going to be when x is zero we get y is equal to nine and so we have the 90.9. Alright, so if we scroll down a little bit and we draw our axes, I will call this point over here negative 1.8. We'll call this up here positive nine. Okay those are points of interest. We know this is gonna be a line, we're just gonna connect those two points with a line. Okay and it has a positive slope so that makes sense. This is what we're drawing, our line is gonna look like this. Alright, So if we go back up to our answer choices, we see an A. We have the equation Y is equal to five X plus nine. Which is the equation we found. Okay we have this graph with a line with positive slope. It has an X intercept at negative 1.8 and a Y intercept at nine. So that's exactly the graph we drew. And so we have answer a here, that's it for this one. I hope this video helped see you in the next one

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In Exercises 47–50, write each English sentence as an equation in two variables. Then graph the equation. The y-value is the difference between four and twice the x-value.