# Thread: Challenging slope, point problem I need help with.

1. ## Challenging slope, point problem I need help with.

So just registered, and was hoping you guys and girls could help me this problem. I have never encountered one like it.

Here it is:

Find the slope of all lines through (7,-4) whose slope is half of its x-intercept.

I would appreciate if anyone could help me. Thanks!

2. ## Re: Challenging slope, point problem I need help with.

Hey mathgeek04.

Hint: The equation of a straight line is y = mx + b = y - y0 = m(x - x0) where (x0,y0) is a point on the line.

3. ## Re: Challenging slope, point problem I need help with.

Originally Posted by chiro
Hey mathgeek04.

Hint: The equation of a straight line is y = mx + b = y - y0 = m(x - x0) where (x0,y0) is a point on the line.
Just to clarify: Those are not all equal... y = mx + b is the slope-intercept form of the line. y-y_0 = m(x - x_0) is the point-slope form of a line. But, mx + b does not equal y - y_0 unless y_0 = 0.

Edit: Since you are given a point, I would recommend using point-slope form for the line.

4. ## Re: Challenging slope, point problem I need help with.

I understand what slope-intercept form is and I understand what point-slope form is, but what do I do with that?

5. ## Re: Challenging slope, point problem I need help with.

Do you know what an x-intercept is?

6. ## Re: Challenging slope, point problem I need help with.

Originally Posted by SlipEternal
Do you know what an x-intercept is?
Yes, it is the point where y is 0 so it it (x,0)

7. ## Re: Challenging slope, point problem I need help with.

Exactly. So, write out the equation for a line in point-slope form (with the point you are given). The x-intercept for the line will be (2m,0) (since the problem tells you the slope is half of the x-intercept). Use that. Plug in y=0, x=2m and solve for m.

8. ## Re: Challenging slope, point problem I need help with.

Thanks for clearing that up, but I do hope it was obvious what was meant to be conveyed.

9. ## Re: Challenging slope, point problem I need help with.

Originally Posted by SlipEternal
Exactly. So, write out the equation for a line in point-slope form (with the point you are given). The x-intercept for the line will be (2m,0) (since the problem tells you the slope is half of the x-intercept). Use that. Plug in y=0, x=2m and solve for m.
Okay so,

y+4=m(2m-7)
4=2m^2-7m
2m^2-7m-4=0
m=4 and m=-0.5

Is that correct?

10. ## Re: Challenging slope, point problem I need help with.

Correct. So, the two lines are:

y+4 = 4(x-7)

and

y+4 = -0.5(x-7)

11. ## Re: Challenging slope, point problem I need help with.

Originally Posted by SlipEternal
Correct. So, the two lines are:

y+4 = 4(x-7)

and

y+4 = -0.5(x-7)

Thank you, so much!