Given: y=4x+3
The slope of a line is the ratio of unit change in y to unit change in x.
In other words, the slope means that, if x increases 1 unit, how much y increases or decreases
its quantity. So that the slope reveals how steeply or slowly the graph goes up or down.
Write standard form of a linear equation in functional form, e.g. y=f(x)=mx+b···Eq.1
In Eq.1, if x increases 1 unit, then y=f(x+1)=m(x+1)+b=mx+m+b···Eq.2
So, the unit change in y is: Eq.2-Eq.1=f(x+1)-f(x)=m
Thus, the slope, the ratio of unit change, is: y : x = m : 1
Therefore, the slope of line y=mx+b is equal to m.
That is: m, the coefficient of x, indicates the slope.
In this question, 4 corresponds to m. So, the slope is 4.
The answer: The slope of line y=4x+3 is 4.