Question

write normal equations for the curve fitting y=a+bx​

Answer 1

Answer:

Step-by-step explanation:

Straight line equation is y=a+bx.

The normal equations are

∑y=an+b∑x

∑xy=a∑x+b∑x2

Answer 2

Concept:

The normal line is defined as the line that is perpendicular to the tangent line at the point of tangency.

Normal=$-\frac{1}{slope\ of\ tangent}$

For an equation by=mx+c

Slope of equation,

$m=\frac{by-c}{x}$

Given:

The equation of a curve y=a+bx.

To find:

The normal of the given equation.

Solution:

From the given equation,

y=bx+a

We can find out that the slope of tangent will be b,

$b=\frac{y-a}{x}$

Now the normal equation n, will be,

$n=-\frac{1}{b}$

⇒$n=-\frac{1}{\frac{y-a}{x} }$

⇒$n=-\frac{x}{y-a}$

Therefore the normal equation of y=a+bx is $-\frac{x}{y-a}$.