Understanding slopes of different equations

The slope of a graph is how steeply it rises or falls, and whether it stays the same tells you the type of function.
A slope that never changes belongs to a straight line; a slope that changes belongs to a curve.

A linear function $y = mx + c$ has a constant slope $m$.
Every time $x$ increases by $1$, $y$ changes by the same amount $m$, which is why its graph is a straight line.
Even $y = xa^b$ is linear, because $a^b$ is just a constant playing the role of $m$.

A quadratic function $y = ax^2 + b$ does not have a constant slope.
Its graph is a U-shape (or an upside-down U), so it falls and then rises, meaning the steepness changes from point to point.
The slope is different everywhere along the curve.

An exponential function $y = ab^x$ also has a changing slope.
It grows (or decays) by a constant factor rather than a constant amount, so each step in $x$ multiplies $y$, making the curve steepen or flatten.
Adding a constant, as in $20 + 1.1^x$, shifts it up but does not make the slope constant.

Which function does NOT have a constant slope?
(A) $f(x) = 20 + 3.46x$
(B) $f(x) = 20 \times 1.1^x$
Choice (A) is in the form $mx + c$ with $m = 3.46$, so its slope is constant.
Choice (B) is exponential, of the form $ab^x$, so its slope changes; (B) is the answer.

Which function has a constant slope?
(A) $f(x) = x^2 + 3$
(B) $f(x) = 4x$
Choice (A) is quadratic, so its U-shaped graph has a changing slope.
Choice (B) is of the form $mx$, a straight line with slope $4$, so (B) has the constant slope.

Is $f(x) = 20 + 1.1^x$ a constant-slope function?
(A) yes
(B) no
The $1.1^x$ term is exponential, and adding $20$ only shifts the graph up without straightening it.
So the slope still changes, and the answer is (B), no.