Question

In the figure above, line $l$ intersects the x-axis at $x=-2$ and the y-axis at $y=-3$. If line m (not shown) passes through the origin and is perpendicular to line $l$, what is the slope of line m ?

• A. $\frac{2}{3}$
• B. $-\frac{3}{2}$
• C. $\frac{3}{2}$
• D. $-\frac{2}{3}$

Answer 1

Answer: (A)

$\frac{2}{3}$

Given

Line ${}^{\prime }{l}^{\prime }$ intersects the x-axis at $x$ $=$ $-2$ and intersects the y-axis at $y$ $=$ $-3$.

We know that

$y$ $=$ $0$ on the x-axis

$x$ $=$ $0$ on the y-axis

Hence, it passes through the points $(-2,$ $0)$ and $(0,$ $-3)$

We know that

If a line passes through the points $(x,$ $y)$ and $(a,$ $b)$, then slope of the line is $\frac{(y-b)}{(x-a)}$.

Slope of the line ${}^{\prime }{l}^{\prime }$ $=$ $\frac{(0-(-3\left)\right)}{\left(\right(-2)-0)}$

$=$ $\frac{-3}{2}$

We know that

If ${}^{\prime }{m}^{\prime }$ and ${}^{\prime }{n}^{\prime }$ are the slopes of two perpendicular lines, then $mn$ $=$ $-1$

To find the slope of the line with slope ${}^{\prime }{m}^{\prime }$ perpendicular to the line ${}^{\prime }{l}^{\prime }$,

$m$ $\times$ $\frac{-3}{2}$ $=$ $-1$

$m$ $=$ $\frac{2}{3}$

$m$ $=$ $0.667$

Therefore, the slope line ${}^{\prime }{m}^{\prime }$ is ${}^{\prime }{0.667}^{\prime }$.