Respuesta :
Answer:
"They are perpendicular because they have slopes that are opposite reciprocals of −5 and one fifth."
Step-by-step explanation:
These lines are both in a form called point-slope form which is
[tex]y-y_1=m(x-x_1)[/tex] where m is slope and [tex](x_1,y_1)[/tex] is a point on the line.
If we determine the slopes are opposite reciprocal, then we have determine the lines are perpendicular.
[tex]y-y_1=m(x-x_1)[/tex]
y − 4 = −5(x − 1), we see the m is -5.
The slope of this line is -5.
[tex]y-y_1=m(x-x_1)[/tex]
y − 4 = one fifth(x − 5), we see the m is (1/5).
The opposite reciprocal of -5 is 1/5 so theses lines are perpendicular.
The slope of the gradient of the line is a number that describe both the direction and the steepness of the line. The given question they are perpendicular because they have slopes that are opposite reciprocals of -5 and one fifth. Thus option 2 is the correct option.
Given-
Equation of the line is,
[tex]y-4=-5(x-1)[/tex]
What is the slope of the line?
The slope of the gradient of the line is a number that describe both the direction and the steepness of the line
Statement given in the question are,
- They are perpendicular because they have slopes that are opposite reciprocals of 5 and negative one fifth.
- They are perpendicular because they have slopes that are opposite reciprocals of -5 and one fifth.
- They are parallel because they have the same slope of 5.
- They are parallel because they have the same slope of negative one fifth.
The standard line of equation can be given as,
[tex](y-y_1)=m(x-x_1)[/tex]
Compare the above equation with the given equation we get the of m is -5.
Thus the slope of the given line is -5. The opposite reciprocal of -5 is 1/5.
Put in the equation,we get,
[tex](y-4)=\dfrac{1}{5}(x-5)[/tex]
Hence, for the given question they are perpendicular because they have slopes that are opposite reciprocals of -5 and one fifth. Thus option 2 is the correct option.
Learn more about the slope of the line here;
https://brainly.com/question/2514839
