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:
-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: $-1$