Question

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

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

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at (0, 3), so the y-intercept \( b = 3 \). This eliminates options b (\( y = 3x + \frac{1}{2} \)) and d (\( y = 3x + 2 \)) since their y-intercepts are \( \frac{1}{2} \) and 2, respectively.

Step2: Calculate slope

Use two points, e.g., (-6, 0) and (0, 3). Slope \( m = \frac{3 - 0}{0 - (-6)} = \frac{3}{6} = \frac{1}{2} \).

Step3: Match equation

The slope-intercept form is \( y = mx + b \). With \( m = \frac{1}{2} \) and \( b = 3 \), the equation is \( y = \frac{1}{2}x + 3 \), which is option c.

Answer:

c) \( y = \frac{1}{2}x + 3 \)