Question

Which of the following is NOT a solution of the equation represented by the graph?
graph shows a line passing through (-3.8,0) (0,-4)


(1 point)
Responses

(2, -7)
(2, -7)

(-5, 4)
(-5, 4)

(0,-4)
(0,-4)

(-2, -1)

Answer 1

To determine which of the provided points is NOT a solution of the equation represented by the graph, we need to find the equation of the line that passes through the points \((-3.8, 0)\) and \((0, -4)\).

1. **Find the slope of the line**:
The slope \(m\) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \((-3.8, 0)\) as \((x_1, y_1)\) and \((0, -4)\) as \((x_2, y_2)\):
\[
m = \frac{-4 - 0}{0 - (-3.8)} = \frac{-4}{3.8} = -\frac{40}{38} = -\frac{20}{19}
\]

2. **Use point-slope form of the line**:
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
Using point \((0, -4)\):
\[
y - (-4) = -\frac{20}{19}(x - 0)
\]
Simplifying this:
\[
y + 4 = -\frac{20}{19}x
\]
\[
y = -\frac{20}{19}x - 4
\]

3. **Test the points** to see if they are solutions of the line's equation \(y = -\frac{20}{19}x - 4\).

- **For (2, -7)**:
\[
y = -\frac{20}{19}(2) - 4 = -\frac{40}{19} - 4 = -\frac{40}{19} - \frac{76}{19} = -\frac{116}{19} \approx -6.1 \quad \text{(not -7)}
\]
- **For (-5, 4)**:
\[
y = -\frac{20}{19}(-5) - 4 = \frac{100}{19} - 4 = \frac{100}{19} - \frac{76}{19} = \frac{24}{19} \approx 1.26 \quad \text{(not 4)}
\]
- **For (0, -4)**:
\[
y = -\frac{20}{19}(0) - 4 = -4 \quad \text{(valid)}
\]
- **For (-2, -1)**:
\[
y = -\frac{20}{19}(-2) - 4 = \frac{40}{19} - 4 = \frac{40}{19} - \frac{76}{19} = -\frac{36}{19} \approx -1.89 \quad \text{(not -1)}
\]

Based on the calculations:

- \( (2, -7) \) does not satisfy the equation.
- \( (-5, 4) \) does not satisfy the equation.
- \( (0, -4) \) satisfies the equation.
- \( (-2, -1) \) does not satisfy the equation.

Now, to answer the question: the points that are NOT solutions are \( (2, -7) \), \( (-5, 4) \), and \( (-2, -1) \). Since the problem asks for one, we can say **(2, -7)** or **(-5, 4)**.

Since we need to choose only one:

The final answer is **(2, -7)**.