xy plane

beater wrote:In the xy-plane, if line k has negative slope and passes through the point (-5,r), is the x intercept of line k positive?

1. the slope of line k is -5
2. r > 0

Please support your answers with explanations. Thanks!

y = mx+b , where m is the slope

X intercept of the line is at (X,0) so :

0 = mx+b

x= -b/m

so we will try to find out whether -b/m is positive or not.

1) m=-5 no info given for b

r = (-5)(-5)+b

r = 25+b

b=r-25 We dont know what r is so we can not decided whethjer -b/m is postive = 25-r/-5

2) r > 0

r = -5m+b



-5m+b > 0

b > 5m

5m is a negative value since We know that slope is NEGATIVE

so we can not decide whether b is positive or negative

INSUF

Statement 1 & 2

r = 25+b

25+b > 0

b > -25

It could be Postie or Negative

So I would go with E

In the xy-plane, if line k has negative slope and passes through the point (-5,r), is the x intercept of line k positive?

1. the slope of line k is -5
2. r > 0

equation of a line

Y = MX + C

given that m = -ve

r = -5m + c

c = r+5m

x intercept is - c/m


now since m is negative , c has to be postive to make the intercept postive

r+5m

1) m = -5

r -25

no idea about r


2) r > 0

still no clue

togther too we cannot find...

IMO E

beater wrote:In the xy-plane, if line k has negative slope and passes through the point (-5,r), is the x intercept of line k positive?

1. the slope of line k is -5
2. r > 0

We need to determine whether the x-intercept of line k is positive, given that line k has a negative slope and passes through the point (-5, r).

We can let the slope of line k be m and the x-intercept of line k be a; that is, line k passes through the point (a, 0). Using the slope formula m = (y2 - y1)/(x2 - x1), we have:

m = (0 - r)/(a -(-5))= -r/(a + 5)

Statement One Alone:

The slope of line k is -5.

Using the information in statement one, we can say the following:

-r/(a + 5) = -5

a + 5 = r/5

a = r/5 - 5

Since we don't know the value of r, we cannot determine the value of a.

For example, if r = 5, a = -4, which is negative. However, if r = 50, a = 5, which is positive. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

r > 0

Knowing r is positive does not give us enough information to determine whether a, the x-intercept of line k, is positive. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Looking at our work from statement one, and keeping in mind that r > 0 from statement two, we see that a can be positive or negative.

For example, if r = 5 then a = -4, which is negative. However, if r = 50 then a = 5, which is positive. The two statements together are still not sufficient to answer the question.

Answer: E