The line passing through $$ (-2,5) $$ and $$ (2, p) $$ has a gradient of $$ -\frac{1}{2} $$. Find the value of $$ p $$. $$ heta p=\square $$ Submit Answer

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The line passing through $$ (-2,5) $$ and $$ (2, p) $$ has a gradient of $$ -\frac{1}{2} $$. Find the value of $$ p $$. $$ 	heta p=\square $$ Submit Answer

UpStudy AI · Accepted Answer

To find the value of $$ p $$, we'll use the formula for the gradient (slope) of a line passing through two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$:

$$
\text{Gradient} = \frac{y_2 - y_1}{x_2 - x_1}
$$

Given the points $$(-2, 5)$$ and $$(2, p)$$ with a gradient of $$-\frac{1}{2}$$, we can set up the equation:

$$
-\frac{1}{2} = \frac{p - 5}{2 - (-2)} = \frac{p - 5}{4}
$$

Now, solve for $$ p $$:

$$
-\frac{1}{2} = \frac{p - 5}{4} \
-2 = p - 5 \quad (\text{Multiply both sides by } 4) \
p = 3
$$

**Answer:**  
$$ p = 3 $$
$$ p = 3 $$

The line passing through and has a gradient of .
Find the value of .

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The line passing through and has a gradient of . Find the value of . Submit Answer