Step-by-step explanation:
Symbolic representation here means defining the function using variables such as x and y (or f(x)).
An example would be f(x) = 4x+3.
Here, we are given two points on the linear function (which is a line), namely
f(4)=5, which implies P1(4,5) is a point P1 on the line, and
f(-7)=5, which implies P2(-7,5) is another point P2 on the line.
With the usual notation that
P1 has the coordinates (x1,y1)
P2 has the coordinates (x2,y2),
we see that
x1=4, y1=5
x2=-7, y2=5
which can be used in the standard equation for a line given two points P1 and P2:
m = slope = (y2-y1)/(x2-x1) = (5-5)/(-7-(4)) = 0/11 = 0
equation of the line
y = m(x-x1) + y1, which simplifies to
y = 0(x-4) + 5, which further simplifies to
y=5 (which is a horizontal line).
