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:
Identify the y-intercept of the graphed line:
Identify the slope of the line given by the equation:
Identify the y-intercept of the line given by the equation:

Answer 1

To analyze the line that goes through the points (0, 1) and (3, 0), let's calculate the slope and y-intercept:

1. **Identifying the slope of the graphed line through the 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 \((x_2, y_2) = (3, 0)\):
\[
m = \frac{0 - 1}{3 - 0} = \frac{-1}{3}
\]

2. **Identifying the y-intercept of the graphed line**:
- The y-intercept is the value of y when x = 0. From the point (0, 1), the y-intercept is:
\[
y = 1
\]

3. **Identifying the slope of the line given by the equation \(y = \frac{1}{2}x - 1\)**:
- The equation is in slope-intercept form \(y = mx + b\), where \(m\) is the slope. Therefore, the slope is:
\[
m = \frac{1}{2}
\]

4. **Identifying the y-intercept of the line given by the equation \(y = \frac{1}{2}x - 1\)**:
- The y-intercept \(b\) can be directly read from the equation. Thus, the y-intercept is:
\[
b = -1
\]

### Summary:
- **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**: \(-1\)