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. (4 points)

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

Answer 1

ohh because where they inersect their x and y values are the same

Answer 2

oooo ok

Answer 3

if they y values are the same then you can equate these 2 equations

y = 8x and y = 2x + 2
8x=2x+2

Answer 4

Because they're both " y = something", you can substitute them into each other.

\(\ \sf \color{blue}{y =} \color{red}{8x}\) and \(\ \sf \color{blue}{y = } 2x + 2 \)

\(\ \sf \color{red}{8x} = 2x + 2 \)

Answer 5

let me fix up the equation though its messed up

Answer 6

for part A:\[ y = 8^x\] \[ y = 2^{x+2}\] for part B
\[8^x = 2^{x+2}\]
for part C:
\[8^x = 2^{x + 2 }\]

Answer 7

As for part B,

you can make a table, first make a function. Like last time, remember that y = f(x) and f(x) = y.

That being said, y = 8x ==> f(x) = 8x, now make a table with x values of -3 to 3.

when x = 2, f(2) = 8(2) = 16 therefore f(2) = 16 for the first function.



The point in this is to see when they both have the same y value, when they do, they're both equal to each other. That's when they intersect.