Question

A straight line passing through point $\left(2,3\right)$ have a slope $\alpha$. What will be the value of $\alpha$ (slope) at point $\left(-2,2\right)$ ?

• A. $4$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{2}{3}$

Answer 1

The correct option is C $\frac{1}{4}$

We know, point-slope form is: (y – y₁) = m(x – x₁)

Putting the values of m, x₁ and y₁ in the equation we get,

⇒ (y – 3) = ($\alpha$)(x – 2)
Now, we have to find slope at $\left(-2,2\right)$.

So, putting the values of $xandycoordinate$ in the equation of straight line we get
$\Rightarrow \left(2-3\right)=\alpha \left(-2-2\right)\Rightarrow \alpha =\frac{1}{4}$