Respuesta :
the slope given by Vladmir's points = (9--3)/10--5) = 12/15 = 4/5
so its equation is
y - y1 = (4/5)(x - x1) where (x1,y1) = (10,9) giving:-
y - 9 = (4/5)(x - 10)
y = 4/5 x =1 which is the required equation
So Vladimir is right.
Testing if Robyn is right:-
Plug in his values:-
-7 = 4/5*-10 + 1
-7 = -7 so that point is on the line
-11 = (4/5) * -15 + 1
-11 = -11 so this point is also on the line
Answer:- c) Both are right
so its equation is
y - y1 = (4/5)(x - x1) where (x1,y1) = (10,9) giving:-
y - 9 = (4/5)(x - 10)
y = 4/5 x =1 which is the required equation
So Vladimir is right.
Testing if Robyn is right:-
Plug in his values:-
-7 = 4/5*-10 + 1
-7 = -7 so that point is on the line
-11 = (4/5) * -15 + 1
-11 = -11 so this point is also on the line
Answer:- c) Both are right
The equation of a line is the equation that models the points on the line.
Both Vladimir and Robyn are correct
Vladimir's claim
The points are given as:
[tex]\mathbf{(x_1,y_1) = (-5,-3)}[/tex]
[tex]\mathbf{(x_1,y_1) = (10,9)}[/tex]
First, we calculate the slope (m)
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{9--3}{10--5}}[/tex]
[tex]\mathbf{m = \frac{12}{15}}[/tex]
Simplify
[tex]\mathbf{m = \frac{4}{5}}[/tex]
The equation is then calculated as:
[tex]\mathbf{y = m(x - x_1) + y_1)}[/tex]
So, we have:
[tex]\mathbf{y = \frac 45(x - -5) -3)}[/tex]
[tex]\mathbf{y = \frac 45(x+5) -3)}[/tex]
Open bracket
[tex]\mathbf{y = \frac 45x+4 -3)}[/tex]
[tex]\mathbf{y = \frac 45x+1}[/tex]
The above equation means that: Vladimir is right
Robyn's claim
We calculated the equation as:
[tex]\mathbf{y = \frac 45x+1}[/tex]
The points are given as:
[tex]\mathbf{(x,y) = (-10,-7)}[/tex]
[tex]\mathbf{(x,y) = (-15,-11)}[/tex]
Substitute these values in the equation.
[tex]\mathbf{(x,y) = (-10,-7)}[/tex]
[tex]\mathbf{y = \frac 45x+1}[/tex] becomes
[tex]\mathbf{-7 = \frac 45 \times -10 + 1}[/tex]
[tex]\mathbf{-7 = -8 + 1}[/tex]
[tex]\mathbf{-7 = -7}[/tex] -- this is true
[tex]\mathbf{(x,y) = (-15,-11)}[/tex]
[tex]\mathbf{y = \frac 45x+1}[/tex] becomes
[tex]\mathbf{-11 = \frac 45 \times -15 + 1}[/tex]
[tex]\mathbf{-11 = -12 + 1}[/tex]
[tex]\mathbf{-11 = -11}[/tex] -- this is also true
The above equations mean that: Robyn is also right
Hence, both Vladimir and Robyn are correct
Read more about equations of straight lines at:
https://brainly.com/question/21627259
