Answer to Question #175702 in Algebra for Thembekile Dlamini

Question #175702

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


1
Expert's answer
2021-04-14T10:00:15-0400

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

Taking log on both sides,

lny=lna+bx×lnelny=lna+bxlny=bx+lnalny=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)(yx)=a(y+x)(y-x)=a

y2x2=ay^2-x^2=a

Let y2=Yand x2=Xy^2=Y and \ x^2=X

Then, YX=aY-X=a

Y=X+a\Rightarrow Y=X+a

 On comparing we get

Slope= 1 and y-intercept= a


3.) y=acos2x+bsin2xy=acos^2x+bsin^2x\\

Let cosx=t theny=at2+b(1t2)y=(ab)t2+by=(ab)cos2x+b\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 cos2x=Xcos^2x=X

Y= (a-b)X +b

On comparing we get

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


4.)

yx2=cTaking log on both sideslny+2lnx=lncLet lny=Y and lnx=XY+2X=lncY=2X+lncyx^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



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