SOLUTION: The line joining A (1, 4) to B (5, p) has a gradient of 1/2. Find the value of p.

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Question 1161549: The line joining A (1, 4) to B (5, p) has a gradient of 1/2. Find the value of p.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
.

The starting basic equation is THIS

    %28p-4%29%2F%285-1%29 = 1%2F2        <<<---=== it is simply the DEFINITION of the slope, or the gradient . . . 


Simplify it and solve for "p"

    %28p-4%29%2F4 = 1%2F2

    p - 4 = 2
  
    p = 2 + 4 = 6.    ANSWER

Solved.

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For this kind of problems, see the lessons
    - Find the slope of a straight line in a coordinate plane passing through two given points
    - Equation for a straight line having a given slope and passing through a given point
    - Solving problems related to the slope of a straight line
    - Equation for a straight line in a coordinate plane passing through two given points
    - Equation for a straight line parallel to a given line and passing through a given point
    - Equation for a straight line perpendicular to a given line and passing through a given point
    - Advanced problems on finding equations for straight lines

    - OVERVIEW of lessons related to the slope of a straight line

Consider these lessons as your textbook,  handbook,  tutorials and  (free of charge)  home teacher.



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


I always recommend students to understand what slope means, instead of relying on memorizing the formula for the gradient between two points.

Gradient (slope) is the ratio of "rise" to "run" -- the change in y compared to the change in x.

Literally, thinking in terms of the gradient or slope of a road, it is a comparison of how far you go up or down (rise = change in y) to how far you go forward (run = change in x).

Using that understanding....

The change in x from A to B is +4.

Since the gradient is 1/2, the change in y from A to B is 1/2 of 4, or 2.

So p is 4+2 = 6.