A(x_2,0)

B(x_1,0)

text

C (x₂,y₂)

E(x₁,y₁)

tanθ = \frac{opposite\ side}{adjacent\ side } = \frac{CD}{DE}= \frac{y_2-y_1}{x_2-x_1

trig function

F(0,y_2)

G(0,y_1)

points

Slope of a function 

The slope of a function is defined as the process
of finding change in the dependent variable of the
function with  respect to that of the independent variable. 

definition

f(x) = (2 * x) + 1
u = 5 (slider from 2.3 to 5, step 0.001)
l = 1.99 (slider from 0.2 to 1.99, step 0.001)
A: (u, 0)
B: (l, 0)
C: (u, f(u))
E: (l, f(l))
g = Segment(E, B)
h = Segment(C, A)
i = OrthogonalLine(E, h)
D = Intersect(h, i)
j = Segment(E, D)
k = Segment(C, D)
distanceCD = Distance(C, D)
distanceED = Distance(E, D)
text6: "Δx=" + j + ""
text7: "Δy=" + k + ""
v = Vector(E, D)
w = Vector(C, D)
function = false
slope = false
a: k / j
b = false
θ = Angle(D, E, C)
text4: "slope =  \frac{rise}{run}= tan θ= \frac{y_2-y_1}{x_2-x_1
}=\frac{Δy}{Δx}\ =\frac{" + (LaTeX[k]) + "}{" + (LaTeX[j]) + "}= " + (LaTeX[a]) + ""
c = false
m = OrthogonalLine(C, yAxis)
F = Intersect(m, yAxis)
G = Intersect(i, yAxis)
n = Segment(F, C)
p = Segment(G, E)
d = false
e = true
t1, d_1, e_1, c_1 = Polygon(E, C, D)
text1: "y = f(x)= " + (LaTeX[f]) + ""