Answer:
The required graph of the equation is shown below:
Step-by-step explanation:
Consider the provided equation.
[tex]4x + 2 = x + 3[/tex]
Solve the equation for x.
[tex]4x-x=3-2[/tex]
[tex]3x=1[/tex]
[tex]x=\frac{1}{3}[/tex]
Now substitute x=1/3 in [tex]y=4x + 2[/tex]
[tex]y=\frac{4}{3} + 2=\frac{10}{3}[/tex]
So, the graph will be the lines which intersect at (1/3,10/3)
The correct graph is 3rd one.
Alternate method:
The equation [tex]4x + 2 = x + 3[/tex] can be written as:
[tex]y= 4x + 2 \\y= x + 3[/tex]
Draw the graph for both equation.
For [tex]y= 4x + 2[/tex]
Substitute x=0 in above equation,
[tex]y= 4(0) + 2[/tex]
[tex]y=2[/tex]
Substitute y=0 in above equation,
[tex]0= 4x + 2[/tex]
[tex]-2=4x[/tex]
[tex]x=\frac{-1}{2}[/tex]
Now use the coordinate (0,2) and (-1/2,0) to draw the graph of straight line.
For [tex]y=x + 3[/tex]
Substitute x=0 in above equation,
[tex]y=3[/tex]
Substitute y=0 in above equation,
[tex]0=x + 3[/tex]
[tex]x=-3[/tex]
Now use the coordinate (0,3) and (-3,0) to draw the graph of straight line.
Hence, the required graph of the equation is shown below:
