Question

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 8x and y = 2x + 2 intersect are the solutions of the equation 8x = 2x + 2. (4 points)
Part B Make tables to find the solution to 8x = 2x + 2. Take the integer values of x between -3 and 3.

Part C: How can you solve the equation 8x = 2x + 2 graphically?

Answer 1

Answer:

(A)

As per the given condition.

You have 2 equations for y.

i,e y =8x and y= 2x+2

then, they will intersect at some point where y is the same for both equations.

That is why in equation y=8x you exchange y with other equation you got which is y=2x+2 once you do this you will have

8x = 2x+2  and the solution of which will satisfy both equation.

(B)

8x = 2x + 2

to find the solutions take the integer values of x between -3 and 3.

x = -3 , then

8(-3) = 2(-3) +2

-24 = -6+2

-12 = -4    False.

similarly, for x = -2

8(-2) = 2(-2)+2

-16 = -2   False

x = -1

8(-1) = 2(-1)+2

-8= 0   False

x = 0

8(0) = 2(0)+2

0= 2   False

x = 1

8(1) = 2(1)+2

8= 4   False

x = 2

8(2) = 2(2)+2

16 = 6   False

x = 3

8(3) = 2(3)+2

24 = 8   False

there is no solution to 8x = 2x +2 for the integers values of x between -3 and 3.

(C)

The equations cab be solved graphically by plotting the two given functions on a coordinate plane and identifying the point of intersection of the two graphs.

The point of intersection are the values of the variables which satisfy both equations at a particular point.

you can see the graph as shown below , the point of intersection at x =0.333 and value of y = 2.667

Answer 2

A) At the intersection, the values of of x and y of the equations are the same. Because of this, we can equate their y values to get an equation in the form of only x.

B)
8(-3) = 2(-3) + 2 → -24 =/= -4
8(-2) = 2(-2) + 2 → -16 =/= -2
8(-1) = 2(-1) + 2 → -8 =/= 0
8(0) = 2(0) + 2 → 0 =/= 2
8(1) = 2(1) + 2 → 8 =/= 4
8(2) = 2(2) + 2 → 16 =/= 6
8(3) = 2(3) + 2 → 24 =/= 14
The solution lies between x = 0 and x = 1.

We can graph both equations and find the value of x and y at which they intersect.