Question

Which graph can be used to find the solution for the equation 4x + 2 = x + 3?

Answer 1

The required graph of the equation is shown below:

Explanation:

Consider the provided equation.

`4x + 2 = x + 3`

Solve the equation for x.

`4x-x=3-2`

`3x=1`

`x=(1)/(3)`

Now substitute x=1/3 in
`y=4x + 2`

`y=(4)/(3) + 2=(10)/(3)`

So, the graph will be the lines which intersect at (1/3,10/3)

The correct graph is 3rd one.

Alternate method:

The equation
`4x + 2 = x + 3` can be written as:

`y= 4x + 2 \\y= x + 3`

Draw the graph for both equation.

For
`y= 4x + 2`

Substitute x=0 in above equation,

`y= 4(0) + 2`

`y=2`

Substitute y=0 in above equation,

`0= 4x + 2`

`-2=4x`

`x=(-1)/(2)`

Now use the coordinate (0,2) and (-1/2,0) to draw the graph of straight line.

For
`y=x + 3`

Substitute x=0 in above equation,

`y=3`

Substitute y=0 in above equation,

`0=x + 3`

`x=-3`

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:

Answer 2

option C

Explanation:

to find the solution for the equation 4x + 2 = x + 3, graph the equations

y= 4x+2 and y=x+3

Lets make a table for each equation

x y= 4x+2

-1 4(-1) + 2= -4+2 = -2

0 4(0) + 2= 2

1 4(1) + 2= 6

plot all the points on graph

Lets make table for second equation

x y= x+3

-1 -1+3 = 2

0 0+3 = 3

1 1+3 = 4

Plot the point on the graph and make a line

option C is correct