Question

P

Line m has a y-intercept of cand a slope of 9, where p>0, q> 0, and p + q.
What is the slope of a line that is perpendicular to line m?

-q/p

P/q

q/p

-p/q

Answer 1

So slope of the line m is 9

We know perpendicular lines have slopes negative reciprocal to each other and their product of slopes is -1

• 9m2=-1
• m2=-1/9

If slope of m is p/q then slope of perpendicular line is -q/p and vice versa

Answer 2

`-(q)/(p)`

Explanation:

Slope-intercept form of a Linear Equation:

`y = mx + b`

where:

• m is the slope
• b is the y-intercept

If line m has a y-intercept of c and a slope of p/q, then:

`\textsf{Equation of line m}: \quad y = (p)/(q)x + c`

If two lines are perpendicular to each other, the product of their slopes will be -1.

Let a = slope of the line perpendicular to line m.

`\implies a * (p)/(q)=-1`

`\implies a=-(q)/(p)`

Therefore, the slope of the a line that is perpendicular to line m is:

`-(q)/(p)`