Question

(04.02 MC)

Answer 1

Answer:

The equation in standard form is:

Rx+Py = -PR

Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

where

• m is the slope

• b is the y-intercept

Given

The y-intercept (0, -R)

The x-intercept (−P, 0)

Finding the slope between (0, -R) and  (−P, 0)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(0,\:-R\right),\:\left(x_2,\:y_2\right)=\left(-P,\:0\right)$

$m=\frac{0-\left(-R\right)}{-P-0}$

$m=-\frac{R}{P}$

Thus, the slope between (0, -R) and  (−P, 0) is:

$m=-\frac{R}{P}$

We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

We are given the y-intercept point (0, −R).

Thus, y-intercept b = -R

so substituting b = -R and $m=-\frac{R}{P}$ in the slope-intercept form to determine the line of the equation

$y = mx+b$

$y=-\frac{R}{P}x\:+\:\left(-R\right)$

$y=-\frac{R}{P}x\:-R$

So, the slope-intercept form of the line equation is:

$y=-\frac{R}{P}x\:-R$

Converting the slope-intercept form of the line equation into standard form

As we know that the equation in the standard form is

Ax+By=C

where x and y are variables and A, B and C are constants

As

$y=-\frac{R}{P}x\:-R$

so converting into standard form

Multiply the equation by P

Py = -Rx - PR

Add -Rx to both sides

Rx+Py = -Rx - PR + -Rx

Rx+Py = -PR

Therefore, the equation in standard form is:

Rx+Py = -PR