y = mx + c is the equation of Straight Line. So in this equation 'm' is Slope of line.
Suppose (x1, y1) and (x2, y2) are two points on any line. Rise of this line is the difference between y2 and y1.
Rise = y2 – y1 = ∆ y-----equation 1.
Similarly run of this line is the difference between x1 and x2.
Run = x2 – x1 = ∆ x ------equation 2.
Slope of line is
M = (y2 – y1)/(x2 - x1) ---------equation 3,
Equation 3 shows the slope of line.
In Trigonometry the slope is also defined by tan ⊖.
M = tan ⊖;
So we can say that slope of curve at a Point is equals to Tangent line at that point.
Now we will see how to find the slope of a Quadratic Equation. Suppose there is an Equation of a curve given by 3x2 + 4x + 6 = 0. We have to find out the slope of this curve. There are some steps to find out the slope.
Step 1: Cross out any constants in original equation. Slope is equals to rate of change, we know that constant do not change, their slope equals to zero, so they will not be present in derivative.
Step 2: Differentiate the given equation.
So 3x2 becomes 2(3x1), or 6x and 4x becomes 4. Sample derivative equation now reads 6x + 4 = 0. So slope at the point (1, 16) = 6 *(1) + 4 = 10. Slope at the point (1, 16) will be 10. Similarly we can find the slope of line at any point.