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.
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!
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.
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.