Question

Which equation represents the graph?
(0, 3), (-1, 4)
A. y = -4/5x + 3
B. y = 5/4x + 3
C. y = 3x + 5
D. y = 1/2x - 1

Answer 1

To determine which equation represents the graph based on the points (0, 3) and (-1, 4), we can follow these steps:

1. **Identify the points**:
- The first point (0, 3) indicates that when \(x = 0\), \(y = 3\). This tells us that the y-intercept of the line is 3.
- The second point (-1, 4) tells us that when \(x = -1\), \(y = 4\).

2. **Calculate the slope (m)** between the two points using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, \((x_1, y_1) = (0, 3)\) and \((x_2, y_2) = (-1, 4)\):
\[
m = \frac{4 - 3}{-1 - 0} = \frac{1}{-1} = -1
\]

3. **Write the equation in slope-intercept form (y = mx + b)**. We already found \(b = 3\) (y-intercept), and the slope \(m = -1\):
\[
y = -1x + 3
\]
or
\[
y = -x + 3
\]

4. **Check against the provided options**:
- A. \(y = -\frac{4}{5}x + 3\)
- B. \(y = \frac{5}{4}x + 3\)
- C. \(y = 3x + 5\)
- D. \(y = \frac{1}{2}x - 1\)

None of the provided options matches \(y = -x + 3\). Therefore, it appears none of the given options accurately represent the points (0, 3) and (-1, 4).

**Conclusion**: The correct slope-intercept equation for the given points is \(y = -x + 3\). If those four equations are the only possible answers, none of them is correct based on our calculations.