In the rectangular coordinate system, if the line x = 2y + 5 passes through points (m, n) and (m + 2,n + p), what is the value of p ?

1

Step-by-step explanation:

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

therefore, 2y=x-5

y=-............................................(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

=

collecting like terms,

=

=

=

∴p=1

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute: