Which point is not a solution of the function graphed below?

graph show a line passing through (0,-5) and (2.5,0)

______ is NOT a solution to this function.
answers
(0,-5)
(5,5)
(2,1)
(-2,-9)

1 answer

To determine which point is not a solution of the function represented by the line passing through (0,-5) and (2.5,0), we first need to derive the equation of the line.

  1. Find the slope (m) using the two points (0, -5) and (2.5, 0):

    • Slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-5)}{2.5 - 0} = \frac{5}{2.5} = 2 \).
  2. Use the slope-point form to find the equation of the line. We can use one of the points, such as (0, -5):

    • The equation is of the form \( y - y_1 = m(x - x_1) \):
    • \( y - (-5) = 2(x - 0) \)
    • Thus, \( y + 5 = 2x \) or \( y = 2x - 5 \).

Now we have the equation of the line: \( y = 2x - 5 \).

Next, we will check the given points to see if they satisfy this equation:

  1. For the point (0,-5):

    • \( y = 2(0) - 5 = -5 \) (This is a solution)
  2. For the point (5,5):

    • \( y = 2(5) - 5 = 10 - 5 = 5 \) (This is a solution)
  3. For the point (2,1):

    • \( y = 2(2) - 5 = 4 - 5 = -1 \) (This is NOT a solution)
  4. For the point (-2,-9):

    • \( y = 2(-2) - 5 = -4 - 5 = -9 \) (This is a solution)

Based on this, the point that is NOT a solution to this function is:

(2,1).