Answer:
Reduced equaton is [tex]5x-3y+\frac{28}{3}=0[/tex].
Step-by-step explanation:
Given parametric equation is,
[tex]x=3t-5[/tex] and [tex] y=5t+1[/tex]
Now, [tex]x=3t-5\implies t=\frac{x+5}{3}[/tex] substitute in second equation we get,
[tex]y=\frac{5}{3}(x+5)+1[/tex]
[tex]y=\frac{5}{3}x+\frac{28}{9}[/tex]
[tex]\implies 5x-3y+\frac{28}{3}=0[/tex]
which is the corresponding rectangular equation after eliinating the parameter.
Now consider,
[tex]y=\frac{5}{3}x+\frac{28}{9}[/tex]
Of which,
Slope : [tex]\frac{5}{3}[/tex]
when,
[tex] x=0, y=\frac{28}{9}=3.1[/tex]
[tex] x=1, y=\frac{43}{9}=4.8; x=-1, y=\frac{13}{9}=1.4 [/tex]
[tex] x=2, y=\frac{58}{9}=6.4; x=-2, y=\frac{-2}{9}=-0.2 [/tex]
[tex] x=3, y=\frac{73}{9}=8.1; x=-3, y=\frac{-17}{9}=-1.8 [/tex]
[tex] x=4, y=\frac{88}{9}=9.8; x=-4, y=\frac{-32}{9}=-3.6 [/tex]
[tex] x=5, y=\frac{103}{9}=11.4; x=-5, y=\frac{-47}{9}=-5.2[/tex]
ans so on. Thus sketching th curve will look like given,
