Question

How do you graph \[3x + y < 5\]?

Answer 1

Hint: Here in this question, we have to plot a graph for the given inequality. First, we have to solve or isolate the given inequality for y using algebraic methods and later give the values to the x like 0, 1, 2, 3, … simultaneously we get the values of y. Now we get the coordinates of given equation i.e., \[\left( {x,y} \right)\] by using the coordinates construct the graph and later Shade above the line for a "greater than" (y> or y\[ \geqslant \]) or below the line for a "less than" (y< or y\[ \leqslant \])

Complete step by step solution:
An inequality shows a set of values greater than or less than, our graph will show more than just a dot on a number line or a line on a coordinate plane.
Consider the given linear inequality
\[3x + y < 5\]---(1)
Now, solve the inequality isolate the variable y using the algebraic methods
Subtract \[3x\] on both side of equation (1), then
\[ \Rightarrow \, 3x + y - 3x < 5 - 3x\]
On simplification, we get
\[ \Rightarrow \, y < 5 - 3x\]
To the above inequality give the x values 0, 1, 2, 3, … simultaneously we get the values of y
Put x=0
Then \[ \Rightarrow \, y < 5 - 3\left( 0 \right)\]
\[\therefore \, y < 5\]
Therefore, co-ordinate \[\left( {x,y} \right) = \left( {0,5} \right)\]
Put x=-1
Then \[ \Rightarrow \,y < 5 - 3\left( { - 1} \right)\]
\[ \Rightarrow \, y < 5 + 3\]
\[\therefore \, y < 8\]
Therefore, co-ordinate \[\left( {x,y} \right) = \left( { - 1,8} \right)\]
Put x=1
Then \[ \Rightarrow \, y < 5 - 3\left( 1 \right)\]
\[ \Rightarrow \, y < 5 - 3\]
\[\therefore \, y < 2\]
Therefore, co-ordinate \[\left( {x,y} \right) = \left( {1,2} \right)\]
And so on
Now, the graph of the given linear inequality \[3x + y < 5\] by using the above coordinate points and the inequality is \[ < \] then we have to Shade below the line in the graph.

Note: The graph is plotted x-axis versus y axis. The graph is two dimensional. By the equation of a graph, we can plot the graph by assuming the value of x. we can’t assume the value of y. because the value of y depends on the value of x. Hence, we have plotted the graph.