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 so
lutions 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?
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?
2 answers:
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
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