Challenging slope, point problem I need help with.

• Nov 13th 2013, 04:23 PM
mathgeek04
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!
• Nov 13th 2013, 04:27 PM
chiro
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.
• Nov 13th 2013, 04:31 PM
SlipEternal
Re: Challenging slope, point problem I need help with.
Quote:

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.
• Nov 13th 2013, 04:38 PM
mathgeek04
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?
• Nov 13th 2013, 04:41 PM
SlipEternal
Re: Challenging slope, point problem I need help with.
Do you know what an x-intercept is?
• Nov 13th 2013, 04:42 PM
mathgeek04
Re: Challenging slope, point problem I need help with.
Quote:

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)
• Nov 13th 2013, 04:54 PM
SlipEternal
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.
• Nov 13th 2013, 04:58 PM
chiro
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.
• Nov 13th 2013, 05:00 PM
mathgeek04
Re: Challenging slope, point problem I need help with.
Quote:

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?
• Nov 13th 2013, 05:03 PM
SlipEternal
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)
• Nov 13th 2013, 05:06 PM
mathgeek04
Re: Challenging slope, point problem I need help with.
Quote:

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!