Graph each line. Give the domain and range. -3x + 6 = 0

Question

Accepted Answer

Hey, everyone here we are asked to plot the given line on a rectangular coordinate system. And we are also asked to find its domain and range here. The given line is negative six X plus 42 is equal to zero. Here we have four answer choice options. ABC and D, each of which display a graph of our given line as well as state the domain and range. So to begin solving this problem, we first want to simplify our given equation for the line by solving for X. So first, we can just add six to both sides and we get the equation six X is equal to 42. Now to get X alone, we need to divide both sides by six. And we are left with the simplified equation where X is equal to seven. Now with our simplified equation for our line, we can begin graphing this equation. So first, we need to set up our rectangular coordinate system by first drawing a vertical line to represent our Y axis and then a horizontal line which crosses through it to represent our X axis. And now we have our simplified line where X is equal to seven. So we just need to mark where X is seven on the X axis. And then to graph our line, we just need to draw a vertical line which passes through the 70.70. So here we intersect the X axis at the 0.70. So now with our graph of our line, we can move on to identifying the domain and range. So beginning with our domain, we have our X values being just a single X value where X is equal to seven. And this is shown in our equation as well as our graph where the X value does not change and always stays being equivalent to seven. So our domain is the set of seven. And now for our range. Well, looking at our graph, we see that our vertical line extends from all Y values along all Y values. So extend it extends from negative infinity to positive infinity. Therefore, our range is again from negative infinity to positive infinity. Since all Y values are encompassed by our line. So now with our domain and range identified as well as our line graphed on a rectangular coordinate system, we are left with answer choice A where again our domain is the set of seven and the range is from negative infinity to positive infinity. And we have a graph of the line X is equal to seven. Thanks for watching. I hope you found this video helpful and I'll see you again, next time.

Graph each line. Give the domain and range. -3x + 6 = 0

Key Concepts

Linear Equations

Domain and Range

Graphing Lines

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