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

Explanation:

Step1: Find the slope

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

Step2: Find the y - intercept

The equation of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Substitute the point $(0,2)$ and $m = 1$ into the equation. When $x = 0$ and $y=2$, we get $2=1\times0 + b$, so $b = 2$.

Step3: Write the equation

The equation of the line is $y=mx + b$, substituting $m = 1$ and $b = 2$ gives $y=x + 2$.

Answer:

$y=x + 2$