Question

1. which equation represents line t, shown in the accompanying diagram?

options:
a. $y = 2x + 3$
b. $y = \frac{1}{2}x + 3$
c. $y = 3x + \frac{1}{2}$
d. $y = 3x + 2$

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 3)$, so $b=3$.

Step2: Calculate slope

Use two points $(-5,1)$ and $(5,5)$. Slope $m=\frac{5-1}{5-(-5)}=\frac{4}{10}=\frac{1}{2}$.

Step3: Write line equation

Substitute $m=\frac{1}{2}$ and $b=3$ into $y=mx+b$.

Answer:

B. $y = \frac{1}{2}x + 3$