Find a point on x-axis

[zekester]

Write an equation using one variable and solve the equation to answer the question.
What are the coordinates of point P on the x-axis such that the slope from P to A(1,4) is twice the slope of a line from P to B(9,10).

I am trying to help a 15 year old nephew who is hospital bound with Lukemia. He is trying his best to keep up with school work while undergoing chemo treatments. Any help that any one can provide will be greatly appreciated.

 

[zekester]

I need to add this is a Geometry problem

 

[wjm11]

Write an equation using one variable and solve the equation to answer the question.
What are the coordinates of point P on the x-axis such that the slope from P to A(1,4) is twice the slope of a line from P to B(9,10).

What is it that you and your nephew know or don’t know? Do you know the formula for slope, given two points? Slope , m = (y2-y1)/(x2-x1) for the given points (x1,y1) and (x2,y2).

If you understand that, there is only one other datum to consider; a point on the x-axis will have a “0” for the y value, so we can consider point P to be P(x,0).

The ratio of the two slopes is 2, so we can write the equation

m1/m2 = ((4-0)/(1-x))/((10-0)/(9-x)) = 2

Just solve for x.

Make sense?