Question

Which point does not lie on the function y-8=2(x-3)

Answer 1

The point that does not lie on the function y-8=2(x-3) is (5, 9).

Step-by-step explanation:

The given function is in the form of y - 8 = 2(x - 3), which represents a linear equation in slope-intercept form (y = mx + c). Here, the slope is 2, and the y-intercept is 8. To determine whether a point lies on the function, substitute its x and y values into the equation. Taking the point (5, 9) as an example, substituting x = 5 and y = 9 into the equation y - 8 = 2(x - 3), we get 9 - 8 = 2(5 - 3), simplifying to 1 = 4, which is not true.

Therefore, the point (5, 9) does not satisfy the equation and does not lie on the given function. This conclusion is reached by substituting the x and y values of the point into the equation and observing if the equation holds true or not. In this case, the equation doesn't hold, signifying that the point (5, 9) is not a part of the function's graph.

This method of verification, by plugging in the coordinates of the point into the equation, allows us to determine whether a point lies on a function or not. In this scenario, the point (5, 9) doesn't align with the equation, establishing that it does not lie on the function y - 8 = 2(x - 3).

Answer 2

The point that does not lie on the function is (-2, 2).

Here's how we can verify this:

1. Plot the function:

[Image of the graph of the function y-8=2(x-3)]

2. Plot the points:

[Image of the graph of the function y-8=2(x-3) with the points (-2,2), (4,10), (3,8), and (-4,-6) plotted]

3. Check each point:

(-2, 2): Substituting x = -2 and y = 2 into the equation yields 2 - 8 = 2(-2 - 3), which simplifies to -6 = -10. This is not true, so (-2, 2) does not lie on the function.

(4, 10): Substituting x = 4 and y = 10 yields 10 - 8 = 2(4 - 3), which simplifies to 2 = 2. This is true, so (4, 10) lies on the function.

(3, 8): Substituting x = 3 and y = 8 yields 8 - 8 = 2(3 - 3), which simplifies to 0 = 0. This is true, so (3, 8) lies on the function.

(-4, -6): Substituting x = -4 and y = -6 yields -6 - 8 = 2(-4 - 3), which simplifies to -14 = -14. This is true, so (-4, -6) lies on the function.

Complete the question:

Which point does not lie on the function y-8=2(x-3) ？

Options: (-2,2) (4,10) (3,8) (-4,-6)