Question

The following graph shows two straight lines passing through the origin. Find the slope of Line 2 from the given graph if the product of two slopes of the two lines is -1.

• A. $y=-0.5x$
• B. $y=0.5x$
• C. $y=-1.5x$
• D. $y=1.5x$

Answer 1

The correct option is B $y=0.5x$

The equation given for Line 1 is $y=-2x$

We know that the equation of the line passing through the origin is $y=mx$

Comparing this with the eqaution of Line 1, we get,
$\text{Slope (m) = -2}$

It is also given that the product of slopes of two lines is 1.

So, we can write,

$\text{Slope of line 1}\times \text{Slope of line 2}=1$

$\Rightarrow -2\times \text{Slope of line 2}=-1$

$\Rightarrow \text{Slope of line 2}=\frac{-1}{-2}$

$\Rightarrow \text{Slope of line 2}=\frac{1}{2}$

$\Rightarrow \text{Slope of line 2}=0.5$

Line 2 passes through the origin.

Equation of a line passing through the origin is $y=mx$

$\therefore$ The equation of Line 2 is $y=0.5x$.