Question

Line L goes through points P and Q, whose coordinates are $(0,1)$ and $(b,0)$, respectively. For which of the following values of b is the slope of line L greater than $-\frac{1}{2}$?

• A. $\frac{1}{2}$
• B. $2$
• C. $\frac{3}{2}$
• D. $\frac{5}{3}$
• E. $\frac{5}{2}$

Answer 1

Answer: (E)

$\frac{5}{2}$

The slope of the line l using the given points $(0,1)$ and $(b,0)$.
$slope=\frac{y}{x}=\frac{0-1}{b-0}=\frac{-1}{b}$.
To get the values of b greater than $\frac{-1}{2}$, good approach is to work with the answers by plugging them into the expression for slope above until you get a value greater than $\frac{-1}{2}$.
For example,
If $b=\frac{1}{2}$
Then the slope $=\frac{-1}{b}=\frac{1}{\frac{-1}{2}}=-2$ which is less than $\frac{-1}{2}$.If $b=2$
Then the slope $=\frac{-1}{2}$ which is equal to $\frac{-1}{2}$.If $b=\frac{5}{3}$
Then the slope $=\frac{-1}{b}=\frac{-1}{\frac{5}{3}}=\frac{-3}{5}$ which is less than $\frac{-1}{2}$.
If $b=\frac{5}{2}$
Then the slope $=\frac{-1}{b}=\frac{-1}{\frac{5}{2}}=-\frac{2}{5}$ which is greater than $\frac{-1}{2}$.
Hence,option E is correct.