Question

On a coordinate plane, a line goes through points (0, 1) and (3, 0). Y = one-half x minus 1.
Identify the slope of the graphed line:
-1/3
Identify the y-intercept of the graphed line:
1
Identify the slope of the line given by the equation:
1/2
Identify the y-intercept of the line given by the equation:

Answer 1

To determine the values requested, let's analyze the information step by step.

1. **Slope of the graphed line through points (0, 1) and (3, 0)**:
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, \((x_1, y_1) = (0, 1)\) and \((x_2, y_2) = (3, 0)\).
\[
m = \frac{0 - 1}{3 - 0} = \frac{-1}{3}
\]
So, the slope of the graphed line is \(-\frac{1}{3}\).

2. **Y-Intercept of the graphed line**:
The y-intercept is the point where the line crosses the y-axis. From the point (0, 1), it's clear that the y-intercept is \(1\).

3. **Slope of the line given by the equation \(y = \frac{1}{2}x - 1\)**:
In the equation \(y = mx + b\), \(m\) stands for the slope. Here, \(m = \frac{1}{2}\).

4. **Y-Intercept of the line given by the equation**:
In the equation \(y = \frac{1}{2}x - 1\), the y-intercept \(b\) is \(-1\).

### Summary of Answers:
- Slope of the graphed line: \(-\frac{1}{3}\)
- Y-Intercept of the graphed line: \(1\)
- Slope of the line given by the equation: \(\frac{1}{2}\)
- Y-Intercept of the line given by the equation: \(-1\)