Question

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

Answer 1

Answer:

option C

Step-by-step 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

Answer 2

Answer:

The required graph of the equation is shown below:

Step-by-step explanation:

Consider the provided equation.

$4x + 2 = x + 3$

Solve the equation for x.

$4x-x=3-2$

$3x=1$

$x=\frac{1}{3}$

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

$y=\frac{4}{3} + 2=\frac{10}{3}$

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,

$0= 4x + 2$

$-2=4x$

$x=\frac{-1}{2}$

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: