Question

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.

Answer 1

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

1. **Find the slope (m)** of the line using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Using the points (0, -5) and (2.5, 0):

\[
m = \frac{0 - (-5)}{2.5 - 0} = \frac{5}{2.5} = 2
\]

2. **Use the point-slope form (y - y_1 = m(x - x_1))** to find the equation of the line. Using the point (0, -5):

\[
y - (-5) = 2(x - 0) \Rightarrow y + 5 = 2x \Rightarrow y = 2x - 5
\]

Now, we can use this equation \( y = 2x - 5 \) to evaluate whether specific points are solutions to the function.

You can check different points to see if they satisfy this equation. For example:

- For the point (0, -5):
\[
y = 2(0) - 5 = -5 \quad \text{(solution)}
\]

- For the point (2.5, 0):
\[
y = 2(2.5) - 5 = 5 - 5 = 0 \quad \text{(solution)}
\]

If you provide any potential point you want to check, I can help determine if it is or is not a solution.

For example, if we check the point (1, -3):
\[
y = 2(1) - 5 = 2 - 5 = -3 \quad \text{(solution)}
\]

But if we check the point (1, -2):
\[
y = 2(1) - 5 = 2 - 5 = -3 \quad \text{(-2 is not a solution)}
\]

Please provide specific points you would like to check, and I'll determine which is not a solution!