Mathematics: Line cd passes through points c(3, –5) and d(6, 0). what is the equation of line cd in standard form? 5x + 3y = 18 5x – 3y = 30 5x – y = 30 5x + y = 18

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Line cd passes through points c(3, –5) and d(6,

Ответ:

Cklug2520

09.07.2020

Mathematics

Theequation of line CD passes through points $C\left({3,-5}\right)$ and $D\left({6,0}\right)$ in standard form is $\boxed{\,{\mathbf{5x-3y=30}}}$ and it matches with $\boxed{{\mathbf{OPTION}}\,{\mathbf{B}}}$ .

Further explanation:

It is given that a line passes through points $C\left({3,-5}\right)$ and $D\left({6,0}\right)$ .

The slope of a line passes through points $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}}\right)$ is calculated as follows:

$m=\frac{{{y_2}-{y_1}}}{{{x_2}-{x_1}}}{\text{}}......\left(1\right)$

Here, the slope of a line is denoted as and points are $\left({{x_1},{y_1}}\right)$ and $\left({{x_2},{y_2}}\right)$ .

Substitute for ${x_1}$ , for ${y_1}$ , for ${x_2}$ and for ${y_2}$ in equation (1) to obtain the slope of a line that passes through points $C\left({3,-5}\right)$ and $D\left({6,0}\right)$ .

$\begin{aligned}m&=\frac{{0-\left({-5}\right)}}{{6-3}}\\&=\frac{5}{3}\\\end{aligned}$

Therefore, the slope is $\frac{5}{3}$ .

The point-slope form of the equation of a line with slope passes through point $\left( {{x_1},{y_1}} \right)$ is represented as follows:

$y-{y_1}=m\left({x - {x_1}}\right){\text{}}......\left(2\right)$

Substitute for ${x_1}$ , for ${y_1}$ and $\frac{5}{3}$ for in equation (2) to obtain the equation of line.

$\begin{aligned}y-\left({-5}\right)&=\frac{5}{3}\left({x-3}\right)\\y+5&=\frac{5}{3}\left({x-3}\right)\\3\left({y+5} \right)&=5\left({x-3}\right)\\3y+15&=5x-15\\\end{aligned}$

Further simplify the above equation.

$\begin{aligned}5x-15-3y-15&=0\\5x-3y-30&=0\\5x-3y&=30\\\end{aligned}$

Therefore the equation of line CD is 5x-3y=30 .

Now, the four options are given below.

$\begin{aligned}{\text{OPTION A}} \to 5x+3y&=18\hfill\\{\text{OPTION B}} \to 5x-3y&=30\hfill\\{\text{OPTION C}} \to 5x-y&=30\hfill\\{\text{OPTION D}}\to5x+y&=18\hfill\\\end{aligned}$

From above data, it is observed that OPTION Bmatches with the obtained solution 5x-3y=30 .

Thus, theequation of line CD passes through points $C\left( {3, - 5} \right)$ and $D\left( {6,0} \right)$ in standard form is $\boxed{\,{\mathbf{5x-3y=30}}}$ and it matches with $\boxed{{\mathbf{OPTION}}\,{\mathbf{B}}}$ .