Question

If line L in the xy-coordinate plane has a positive slope, what is the x-intercept of L ? (1) There are different points (a, b) and (c, d) on line L such that ad = bc. (2) There are constants m and n such that the points (m, n) and (–m, –n) are both on line L.

Answer 1

Answer:

The x-intercept of L is 0

Step-by-step explanation:

1)  If (a,b) and (c,d) belongs to theline L, then the equation of the line using two-points formula  will be:

$y-b=(\frac{b-d}{a-c} ).(x-a)$

if we want to find the x-intercept of L we should set y=0.

$0-b=(\frac{b-d}{a-c} ).(x-a)$

getting x from that equation we will have :

$x=-b.\frac{a-c}{b-d}+a$

using distributive propertie and common denominator will be obtain

x= $x= \frac{bc-ad}{b-d}$

as we know that ad=bc the numerator will be equal to zero. Then x=0.

2) Using the same equation of line but using the points(m,n) and (-m, -n) we will set it as:

$y-n=\frac{-2n}{-2m}.(x-m)$

if we want to find the x-intercept of L we should set y=0.

$0-n=\frac{-2n}{-2m}.(x-m)$

getting x from that equation we will have :

$-n=\frac{n}{m}(x-m)$

$x= -n.\frac{m}{n} + m$

them

x = 0