Answer:
y = -x/ 5 + 3/5
Solution:
First, get the x-intercept form of 2x-3y = 6
Para kuhanin yung x intercept form ng isang equation ay sinusubstitutan lang ng 0 si y
so
if y = 0:
2x - 3 (0) = 6
2x = 6
Divide both sides by 2 lang and we'll get
2x/2 = 6/2
x = 3
So 3 ang x - intercept form ni 2x-3y = 6
Then yung coordinates ng x-intercept na iyon ay (3, 0)
Nung nagcocompete kami dati sa math contests gumagamit kami ng shortcut para makuha yung equation ng line perpendicular to the original line
So yun na lang din gagamitin ko para mas madali
Ayon sa shortcut, isusulat muna lang natin si equation ng original line sa kaniyang standard form
Ax + By = C
so
slope-intercept form of the original equation of the line:
y = 5x - 8
Standard form:
8 = 5x - y
5x - y = 8
Then, para makuha yung equation ng line perpendicular to the original line na passing through daw sa x-intercept ng 2x - 3y =6 ay follow these steps lang
1. Pagpalitin yung coefficients ng x at y sa equation na 5x - y
so,
5x - y
=> x - 5y
2. Ibahin yung sign sa gitna nung pinaltang equation
x - 5y
=> x + 5y
3. So ibig sabihin ngayon is meron na tayong left side ng equation ng line perpendicular to the original line
x + 5y =?
Right side na lang yung kulang
4. Para makuha yung right side is gagamitin lang natin yung nacompute nating coordinates ng x-intercept kanina which is yung (3, 0)
Then i susubstirue lang natin itong (3,0) sa bagong equation which is yung x + 5y
So meron tayong
(3, 0)
x = 3 and y = 0:
x + 5y
= (3) + 5(0)
= 3 +0
= 3
Ibig sabihin, itong 3 ang magiging right side ng equation nung line na perpendicular sa original line
so kumpleto na ang ating bagong equation
x + 5y = 3
Then ayon sa tanong ay kailangan lang itong isulat sa kaniyang slope intercept form which is yung y = mx + b
so
Standard form:
x + 5y = 3
Slope-intercept form:
x + 5y = 3
Transpose si x sa opposite side and we'll get:
5y = - x +3
Then, divide both sides by 5
5y/5 = (-x + 3)/ 5
y = -x/ 5 + 3/5
Therefore the equation of the line perpendicular to y = 5x - 8 and is passing through the x-intercept of 2x - 3y = 6 is y = -x/ 5 + 3/5 (in its slope-intercept form)
Final answer: y = -x/ 5 + 3/5
Note: shortcut na rin ginamit ko rito at inexplain para rin sa ibang tao na makababasa ng problem na ito.
If nasaulo mo ang shortcut nato is pwedeng mentalin na yung ganyang uri ng problem in 15 secs.
Another note: may isa pang shortcut na mas madali kesa sa binanggit ko na applicable pag kukuhanin yung equation ng perpendicular line passing through x or y intercept of another equation, pero di ko na ginamit yun kasi magiging weird na (para to sa makababasa ng problem na ito)
Thank you and correct me if merong mali sa solution ko.
Thank you!
