Question

The parametric equation of the line is given by
$x=-2+\frac{r}{\sqrt{10}};y=1+\frac{3r}{\sqrt{10}}$, then for the line

• A. $x$ intercept is $\frac{7}{3}$
• B. $y$ intercept is $7$
• C. slope is $3$
• D. $x$ intercept is $-\frac{7}{3}$

Answer 1

Answer: (B), (C), (D)

The correct options are
B $y$ intercept is $7$
C slope is $3$
D $x$ intercept is $-\frac{7}{3}$

Given
$x=-2+\frac{r}{\sqrt{10}};y=1+\frac{3r}{\sqrt{10}}$
From the above parametric equation we can say that the given line passes through $(-2,1)$ and
$\cos \theta =\frac{1}{\sqrt{10}},\sin \theta =\frac{3}{\sqrt{10}}\Rightarrow \tan \theta =3$
Equation of line
$(y-1)=3(x+2)\Rightarrow y=3x+7$

Hence, the slope of the line is $3$,
$y$ intercept is 7 and $x$ intercept is $-\frac{7}{3}$.