Question

EASY AND BRAINLIEST!!!!
NO NEED TO THINK!!!!!

Line L is perpendicular to the graph of 2x + 3y = 5 and has the same x-intercept as the graph of 2x + 3y = 5. Find the standard form of the equation whose graph is L.

Answer 1

Answer:

$6x-4y=15$

Step-by-step explanation:

step 1

Find the slope of line L

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal

In this problem we have

$2x + 3y = 5$

Isolate the variable y

$3y = -2x+5\\y=-(2/3)x+(5/3)$

The slope of the given line is

$m=-2/3$

so

The slope of the Line L is

$m=3/2$

step 2

Find the x-intercept of the line

$2x + 3y = 5$

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

$2x + 3(0) = 5\\x=5/2$

The x-intercept is the point (5/2,0)

step 3

Find the equation of the line L

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=3/2\\point (5/2,0)$

substitute

$y-0=(3/2)(x-5/2)$

$y=(3/2)x-(15/4)$

Convert to standard form

AX +By+C

where

A is a positive integer

B and C are integers

Multiply both sides by 4

$4y=6x-15\\6x-4y=15$