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

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(3,-5)$ and $(x_2,y_2)=(6,0)$. So $m=\frac{0 - (-5)}{6 - 3}=\frac{5}{3}$.

Step2: Use the point - slope form

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

Step3: Convert to standard form

Expand the point - slope form: $y=\frac{5}{3}x-10$. Multiply through by 3 to get $3y = 5x-30$. Rearrange to standard form $Ax+By = C$: $5x-3y=30$.

Answer:

B. $5x - 3y = 30$