Question

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

Explanation:

Step1: Find the slope (m)

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

Step2: Find the y-intercept (b)

The y-intercept is the value of y when x = 0. From point (0, 2), when x = 0, y = 2, so b = 2.

Step3: Write the equation

The slope-intercept form is $y = mx + b$. Substituting m = 1 and b = 2:
$y = 1x + 2$ or $y = x + 2$

Answer:

$y = x + 2$ (the first option)