Write an equation of the straight line which is perpendicular
1 answer:
Answer:
3x + 2y = 14
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 2x - 3y = 5 into this form by subtracting 2x from both sides
- 3y = - 2x + 5 ( divide all terms by - 3 )
y = x -
← in slope- intercept form
with slope m =
Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
= -
, thus
y = - x + c ← is the partial equation
To find c substitute (4, 1) into the partial equation
1 = - 6 + c ⇒ c = 1 + 6 = 7
y = - x + 7 ← in slope- intercept form
Multiply through by 2
2y = - 3x + 14 ( add 3x to both sides )
3x + 2y = 14 ← in standard form
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Try this solution:
let the unknown two-digits number be 'xy'.
Then it is possible to write any two-digit number as 10x+y, where x - the tens digit and y - the unit digit.
Using the rule described above the phrase 'the tens digit of a number is twice the units digit' may be written as x=2y.
Using the same rule the phrase 'if the digits are reversed, the new number is 36 is less than the original number' may be written as (10x+y)-(10y+x)=36.
These two equations may be resolved as system of two equations:
Check: the original number is 84, the new number is 48; difference is 84-48=36.
answer: 84
let the unknown two-digits number be 'xy'.
Then it is possible to write any two-digit number as 10x+y, where x - the tens digit and y - the unit digit.
Using the rule described above the phrase 'the tens digit of a number is twice the units digit' may be written as x=2y.
Using the same rule the phrase 'if the digits are reversed, the new number is 36 is less than the original number' may be written as (10x+y)-(10y+x)=36.
These two equations may be resolved as system of two equations:
Check: the original number is 84, the new number is 48; difference is 84-48=36.
answer: 84