Question

Statement I The point $(x,y)$ lies on the line with slope $m$ and $y$-intercept $c$, if and only if $y=mx+c$.
Statement II Suppose line $L$ with slope $m$ makes $x$-intercept $d$. The equation of $L$ is $y=(x+d)$.

• A. Both statements are true
• B. Only Statement I is true
• C. Only Statement II is true
• D. Both statements are false

Answer 1

Answer: (B)

I. Suppose a line $L$ with slope $m$ cuts the $Y$-axis at a distance $c$ from the origin. The distance $c$ is called the $y$-intercept of the line $L$. Obviously, coordinates of the point where the line meet the $Y$-axis are $(0,c)$. Thus, $L$ has slope $m$ and passes through a fixed point $(0,c)$. Therefore, by point-slope form, the equation of $L$ is

$y-c=m(x-0)\text{ or }y=mx+c$
Thus, the point $(x,y)$ on the line with slope $m$ and $Y$-Intercept $c$ lies on the line, if and only if $y=mx+C$
Note that the value of $c$ will be positive or negative according as the intercept is made on the positive or negative side of the $Y$-axis, respectively.
II. Suppose line $L$ with slope $m$ makes $x$-intercept ' $d$ ', then coordinate of the point where the line meet the $x$-axis are $(d,0)$. Thus, $L$ has slope ' $m$ ' and passes through fixed point $(d,o)$. Therefore, by point slope form the equation of $L$ is
$y-0=m(x-d)\Rightarrow y=m(x-d)$