Respuesta :
Answer:
a = 1, b = -1 and c = 7
Step-by-step explanation:
Since, when two lines are parallel then the product of their slope is -1,
Also, the slope intercept form of a line is y = mx + c,
Where, m is the slope of the line,
x + y = 2 ⇒ y = -x + 2
Thus, the slope of the line x + y = 2 is -1,
Let [tex]m_1[/tex] is the slope of the line that is perpendicular to x + y = 2,
By the above statement,
[tex]m_1\times -1=-1\implies m_1 = 1[/tex]
Suppose y = x + c is the line perpendicular to the line x + y = 2,
According to the question,
y = x + c is passes through the point (1,-6),
⇒ -6 = 1 + c ⇒ -6 - 1 = c ⇒ c = -7
Hence, the equation of the required line is,
y = x - 7
⇒ x - y = 7
Compare this with standard form of line ax+by=c
We get, a = 1, b = -1 and c = 7
Answer:
The standard form of required line is x-y=7.
Step-by-step explanation:
The standard form of a line is
[tex]ax+by=c[/tex]
Where, a,b,c are integers with no factor common to all three and a≥0.
The give equation of line is
[tex]x+y=2[/tex]
Here a=1 and b=1.
The slope of a standard line is
[tex]m=\frac{-a}{b}[/tex]
[tex]m_1=\frac{-1}{1}=-1[/tex]
The product of slops of two perpendicular lines is -1.
[tex]m_1\cdot m_2=-1[/tex]
[tex](-1)\cdot m_2=-1[/tex]
[tex]m_2=1[/tex]
The slope of required line is 1.
The point slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
Where, m is slope.
The slope of required line is 1 and it passes through the point (1,-6). So, the equation of required line is
[tex]y-(-6)=1(x-1)[/tex]
[tex]y+6=x-1[/tex]
Add 1 on each side.
[tex]y+7=x[/tex]
Subtract y from both the sides.
[tex]7=x-y[/tex]
Therefore the standard form of required line is x-y=7.
