What is the Value of $$ P $$, if the gradent of the line joining $$ [1, p] $$ and $$ [p, 4] $$ is $$ 2 / 3 $$

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To find the value of $$ p $$ given that the gradient (slope) of the line joining the points $$ (1, p) $$ and $$ (p, 4) $$ is $$ \frac{2}{3} $$, follow these steps:

1. **Understand the Slope Formula:**
   
   The slope $$ m $$ between two points $$ (x_1, y_1) $$ and $$ (x_2, y_2) $$ is given by:
   
   $$
   m = \frac{y_2 - y_1}{x_2 - x_1}
   $$
   
2. **Apply the Given Points:**

Substitute the given points $$ (1, p) $$ and $$ (p, 4) $$ into the slope formula:

$$
   \frac{4 - p}{p - 1} = \frac{2}{3}
   $$

3. **Solve for $$ p $$:**

Multiply both sides of the equation by $$ 3(p - 1) $$ to eliminate the denominator:

$$
   3(4 - p) = 2(p - 1)
   $$

Simplify the equation:

$$
   12 - 3p = 2p - 2
   $$

Combine like terms:

$$
   12 + 2 = 2p + 3p
   $$
   
   $$
   14 = 5p
   $$
   
   $$
   p = \frac{14}{5}
   $$

4. **Final Answer:**

The value of $$ p $$ is $$ \frac{14}{5} $$ or $$ 2.8 $$.

**Answer:**  
The value of $$ p $$ is fourteen fifths, that is $$ p = \dfrac{14}{5} $$.
The value of $$ p $$ is $$ \frac{14}{5} $$ or 2.8.

What is the Value of , if the
gradent of the line joining and
is

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