On a coordinate plane, a line goes through points (0, 1) and (3, 0). Y = one-half x minus 1.

Question

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: \(-1\)