Problem Solving

in the xy plane line k has a positive slope and and x-intercept 4. if the area of the triangle formed by line k and the two axes is 12, what is the y intercept of line k

a. -6
b. -4
c. -3
d. 3
e. 6


please explain how you get the right anwser

baller12q wrote:in the xy plane line k has a positive slope and and x-intercept 4. if the area of the triangle formed by line k and the two axes is 12, what is the y intercept of line k

a. -6
b. -4
c. -3
d. 3
e. 6


please explain how you get the right anwser

IMO E
Positive slope cut x in 4 (the line is descending from up left to down right) So the base of the triangle is 4.
Then 4*Y/2=12
Answer y=6
Is a 3-4-5 triangle

Area = 1/2(bh) = 12
.5(4)h=12
h=6

so the absolute value of the y-intercept is 6. We can't know it is positive or negative unless we know more about line k. Since we know it has a positive x-intercept and is positively sloped, its y-intercept is negative.

A

cm47323 wrote:Area = 1/2(bh) = 12
.5(4)h=12
h=6

so the absolute value of the y-intercept is 6. We can't know it is positive or negative unless we know more about line k. Since we know it has a positive x-intercept and is positively sloped, its y-intercept is negative.

A

I agree fully. Thanks for the nice explanation

cm47323 wrote:Area = 1/2(bh) = 12
.5(4)h=12
h=6

so the absolute value of the y-intercept is 6. We can't know it is positive or negative unless we know more about line k. Since we know it has a positive x-intercept and is positively sloped, its y-intercept is negative.

A

I also arrived @ the answer the same way. Well done.

hey could someone explain the reasoning behind the highlighted part ?

cm47323 wrote:Area = 1/2(bh) = 12
.5(4)h=12
h=6

so the absolute value of the y-intercept is 6. We can't know it is positive or negative unless we know more about line k. Since we know it has a positive x-intercept and is positively sloped, its y-intercept is negative.

A

positive slope means the line is always be falling toward x axis
now base is 4;and area is 12 ;therefore ht is 6
since line is having a +ve x intercept and a +slope the line is in 4th quardant
hence ht is -6
A

i get that.
But doesnt a positive slope rise from the 3rd quadrant towards the first quadrant ?

and a negative slope falls in the direction of second quadrant to the fourth quadrant???

If its rising from the 3rd quadrant(being a +ve slope), the positive x intercept would be in the first quadrant....and so would the y intercept be. isnt it ?


Can someone please draw the direction of the slopes ?

thephoenix wrote:positive slope means the line is always be falling toward x axis
now base is 4;and area is 12 ;therefore ht is 6
since line is having a +ve x intercept and a +slope the line is in 4th quardant
hence ht is -6
A

baller12q wrote:in the xy plane line k has a positive slope and and x-intercept 4. if the area of the triangle formed by line k and the two axes is 12, what is the y intercept of line k

a. -6
b. -4
c. -3
d. 3
e. 6


please explain how you get the right anwser

Many members have posted answer as 6.
If the two points are (4,0) and (0,6)
then the slope of the line would be= (y1-y2)/(x1-x2)=(6-0)/(0-4)=6/-4 < 0
but slope is mentioned positive hence, -6 is correct