Question

$\mathbb{ \ \ Q\ U\ E\ S\ T\ I\ O\ N\: \: }$
Consider the line in the coordinate plane that passes through the point (-7, -3) and the origin. Find the slope of a line perpendicular to the line described.​

Answer 1

S O L U T I O N :

• Let , the points be A (0,0) and B (-7,-3) and the given line passes through the points A and B respectively.

T W O - P O I N T slope formula :

$m \: = \dfrac{x1 - x2}{y1 - y2}$

• Here , ( x1 , y1 ) and ( x2 , y2 ) are two points through which line is passing and m is slope of the given line.

Now , by applying this formula : we get ,

$\implies \: m \: = \dfrac{0 - ( - 7)}{0 - ( 3)}$

$\implies \: m \: = \dfrac{7}{3}$

• Now , we need to find the slope of line perpendicular to given line.

• We know that , if two line are perpendicular to each other then product of their slopes is equal to (-1)

So here , Let Slope of another line = m1

$\implies \: m \: \times m1 = - 1$

$\implies \: \frac{7}{3} \times m1 = - 1$

$\implies \: m1 = ( - 1) \dfrac{3}{7}$

$\implies \: m1 = \dfrac{ - 3}{7}$

• Therefore , the slope of required line is (-3/7)

Answer 2

$\green{ \fcolorbox{grey}{grey}{ \checkmark \: \textsf{Verified \: answer}}}$

The slope of required line is (-3/7)