Answer to Question #175702 in Algebra for Thembekile Dlamini

Question

Manipulate the above equations in the form of y=mx+c and find the slope and y- intercept as well

1.y=aexp(bx)

2.(y+x)(y-x)=a

3.y=acosx^2+bsinx^2

4.yx^2=c

Answer 1

1.) $y=ae^{bx}$

Taking log on both sides,

$lny=lna+bx\times lne\\lny=lna+bx\\lny=bx+lna$

Let lny=Y and x=X

Y = bX + lna

on comparing we get

Slope = b and y-intercept = lna

2.) $(y+x)(y-x)=a$

$y^2-x^2=a$

Let $y^2=Y and \ x^2=X$

Then, $Y-X=a$

$\Rightarrow Y=X+a$

 On comparing we get

Slope= 1 and y-intercept= a

3.) $y=acos^2x+bsin^2x\\$

$\text{Let cosx=t then}\\y=at^2+b(1-t^2)\\y=(a-b)t^2+b\\y=(a-b)cos^2x+b$

Let y= Y and $cos^2x=X$

Y= (a-b)X +b

On comparing we get

Slope= (a-b) and y-intercept= b

4.)

$yx^2=c\\\text{Taking log on both sides}\\ lny+2lnx=lnc\\ \text{Let lny=Y and lnx=X}\\Y+2X=lnc\\Y=-2X+lnc$

On comparing we get

Slope= -2 and y-intercept= lnc