Answer
(a) Slope of a linear function is: change in the $y$ coordinates divided by the corresponding change in the $x$ coordinates between two distinct points on the line of this function.
We can find it by the way explained above, or in the equation find $m$:
$y=mx+b$
which stands for the slope.
Rate of change of a linear function is the same as the slope explained above.
(b) Yes, a linear function has the same rate of change for any given interval.
(c) $y=2x+4$
Also see the image below for the graph.
Work Step by Step
(a) Slope of a linear function is a tangent of that line, which means change in the $y$ coordinates divided by the corresponding change in the $x$ coordinate between two distinct points on the line of this function.
One way to find the slope is the way explained above. Another one is using equation of this function:
$y=mx+b$
In the general equation of a linear function, $m$ stands for the slope.
Rate of change of a linear function is the same as the slope explained above.
(b) As we know from the general equation of a linear function, which is ($y=mx+b$), $m$ and $b$ are constants.
A linear function has the same rate of change for any given interval
(c) In the general form of the equation of a linear function, we can simply input anything at position of constants and we will have an example of it. for instance:
$y=2x+4$
Also see the image below for the graph.
