Respuesta :
Answer:
[tex]-4x+y=-5[/tex]
Step-by-step explanation:
It is given that he vector y = ai + bj is perpendicular to the line ax + by = c.
Given given point is P(-1,-9) and given vector is v = -4i + j.
Here, a = -4 and b= 1.
We need to find the equation of the line through P perpendicular to v.
Using the above fact, the vector v = -4i + j is perpendicular to the line
[tex](-4)x+(1)y=c[/tex]
[tex]-4x+y=c[/tex] ... (1)
The line passes through the point (-1,-9).
Substitute x=-1 and y=-9 in the above equation to find the value of c.
[tex]-4(-1)+(-9)=c[/tex]
[tex]4-9=c[/tex]
[tex]-5=c[/tex]
The value of c is -5.
Substitute c=-5 in equation (1).
[tex]-4x+y=-5[/tex]
Therefore the equation of line which passes through P and perpendicular to v is -4x+y=-5.
The line equation is [tex]-4x + y = -5[/tex]
Calculation of Line equation:
Using formula/ standard equation of a line:
[tex]\to ax+by=C[/tex]
[tex]\to a=-4\\\\\to b=1 \\\\\to (-4).x +1.y = C\\\\ \to - 4.x + y = c\\\\[/tex]
When the line passes through [tex](-1,-9)[/tex]:
[tex]\to -4(-1)+(-9) = C\\\\ \to 4+(-9) = C\\\\ \to -5=c\\\\[/tex]
Therefore, the line equation is [tex]-4x + y = -5[/tex].
Find out more information about the line equation here:
brainly.com/question/2564656
