Question

write an equation of the line that passes through a pair of points:
a. $y = x + 3$
b. $y = x - 3$
c. $y = -x + 2$
d. $y = -x - 2$

Explanation:

Step1: Identify the y-intercept

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

Step2: Determine the slope

Using two points, e.g., (0, -3) and (3, 0), the slope \( m = \frac{0 - (-3)}{3 - 0} = \frac{3}{3} = 1 \).

Step3: Write the equation

Using the slope-intercept form \( y = mx + b \), substitute \( m = 1 \) and \( b = -3 \), so \( y = x - 3 \).

Answer:

b. \( y = x - 3 \)