Respuesta :

jenicamuchemwa

Answer:

p = 1

Step-by-step explanation:

Given data:

X = 2y + 5

therefore Y = X/2 - 5/2

Given co-ordinates (m,n) and (m+2,n+p)

Equation of a straight line is represented by Y = mX + C where m is gradient and  c is y intercept

For the given equation y intercept is at (0,-5/2) and gradient is 1/2

Given point (X₁ , Y₁) and (X,Y)

Gradient = (Y - Y₁)/(X-X₁)

Finding gradient using  (m,n) and (m+2,n+p)

1/2=( n+p - n)/m+2-m)

1/2 = p/2 (Multiplying both sides by 2)

p = 1

adetoseen

Answer:

1

Step-by-step explanation:

the equation of the line is given as x=2y +5.................................(1)

therefore, 2y=x-5

y=[tex]\frac{x}{2}[/tex]-[tex]\frac{5}{2}[/tex]............................................(2)

recall, equation of any line is given as

y=mx + c.......................(3)

where m=slope= y₂ - y₁ / x₂ -x₁...............(4)

∴  by comparison of equations 2 and 3

m=1/2

(x₁,y₁)= (m,n)

(x₂,y₂)=(m+2,n+p)

therefore, from equation 4

[tex]\frac{1}{2}[/tex]=[tex]\frac{n+p-n}{m+2-m}[/tex]

collecting like terms,

[tex]\frac{1}{2}[/tex]=[tex]\frac{n-n+p}{m-m+2}[/tex]

[tex]\frac{1}{2}[/tex]=[tex]\frac{0+p}{0+2}[/tex]

[tex]\frac{1}{2}[/tex]=[tex]\frac{p}{2}[/tex]

∴p=1

Otras preguntas