Question

How do you graph x + 2y = 18 using intercept?

Answer 1

Hint: We are given x + 2y = 18, we have to sketch the graph of the function. To do so we will learn about the type of the equation and how their graph is differently formed. Once we have that knowledge we will learn our function is a linear function. So we just need 2 or 3 points that satisfy our equation. Since we are asked to find using the intercept so we first learn about intercepts and then form our graph.

Complete step by step answer:
We have to draw the graph of x + 2y = 18. Now, in our equation, x + 2y = 18, we have x and y are variables and their power is 1. So, we have a linear equation and its graph is a straight line. Now, we have to sketch using an intercept, so we understand the intercept and then we find the intercepts. The intercepts are those points of x – axis and y-axis where the function intersects with x – axis and y – axis. The point where the graph touches the x – axis is called x – intercept. While, the point where the graph touches the y-axis is called the y-axis. Now to find the x-intercept, we put y = 0 in x + 2y = 18. So, we get,
\[x+2\times 0=18\]
\[\Rightarrow x+0=18\]
We get,
\[\Rightarrow x=18\]
So, the x-intercept is at (18, 0).
For y – intercept, we put x = 0 in our equation, so putting x = 0 in x + 2y = 18, we get,
\[\Rightarrow 0+2y=18\]
So, we get,
\[\Rightarrow 2y=18\]
On simplifying, we get,
\[\Rightarrow y=9\]
Hence y-intercept is at (0, 9).
Now, we will put these values on the graph and join them, then the line obtained is our required graph of x + 2y = 18.

Note: While solving the problem, we need to be careful with the calculation part like 6 – 2y = 4, here we cannot say 2y = 4 – 6, we need to see that 2y has ‘–‘ in front of it, so we need to remove it and also we should know dividing a positive term by negative term will always give us a negative term.