line cd passes through points c(3, -5) and d(6, 0). what is the equation of line cd in standard form?\n5x +…

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given $C(3,-5)$ and $D(6,0)$, we have $m=\frac{0 - (-5)}{6 - 3}=\frac{5}{3}$.

Step2: Use the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using point $D(6,0)$ and $m = \frac{5}{3}$, we get $y-0=\frac{5}{3}(x - 6)$.

Step3: Convert to standard form

$y=\frac{5}{3}(x - 6)$ expands to $y=\frac{5}{3}x-10$. Multiply through by 3 to get $3y = 5x-30$. Rearranging gives $5x-3y = 30$.

Answer:

$5x - 3y=30$ (corresponding to the second option)