Question

line cd passes through points (0, 2) and (4, 6). which equation represents line cd?
○ $y = 2x - 2$
○ $y = 2x + 2$
○ $y = x + 2$
○ $y = x - 2$

Explanation:

Step1: Find the slope (m)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). For points \((0, 2)\) (where \(x_1 = 0, y_1 = 2\)) and \((4, 6)\) (where \(x_2 = 4, y_2 = 6\)):
\( m = \frac{6 - 2}{4 - 0} = \frac{4}{4} = 1 \)

Step2: Find the y-intercept (b)

The line equation is \( y = mx + b \). We know \( m = 1 \) and the line passes through \((0, 2)\), so when \( x = 0 \), \( y = 2 \). Substituting into \( y = mx + b \):
\( 2 = 1(0) + b \)
\( b = 2 \)

Step3: Write the equation

Using \( m = 1 \) and \( b = 2 \), the equation is \( y = x + 2 \)

Answer:

C. \( y = x + 2 \) (Note: Here the option with \( y = x + 2 \) is the third option in the given choices)