Assertion (A): Equation of a line with slope $-2$ and intersecting the $x$ axis at a distance of 3 units to the left of origin is $2x - y - 6 = 0$.
Reason (R): Equation of a line passing through the point $(x_{1}, y_{1})$ and with slope $m$ is given by $(y - y_{1}) = m(x - x_{1})

Question

Assertion (A): Equation of a line with slope $-2$ and intersecting the $x$ axis at a distance of 3 units to the left of origin is $2x - y - 6 = 0$.
Reason (R): Equation of a line passing through the point $(x_{1}, y_{1})$ and with slope $m$ is given by $(y - y_{1}) = m(x - x_{1})$.

(a) Both (A) and (R) are true and (R) is the correct explanation of (A)
(b) Both (A) and (R) are true but (R) is not the correct explanation of (A)
(c) (A) is true but (R) is false.
(d) (A) is false but (R) is true.

Accepted Answer

>

> [!TLDR]
> Assertion is false, Reason is true — option (d).
>
> **Reason (R):** The point-slope form $(y-y_1)=m(x-x_1)$ is a correct, standard formula. So (R) is true.
>
> **Assertion (A):** “3 units to the left of origin” on the $x$-axis is the point $(-3,0)$. A line with slope $-2$ through it is
> $$y-0=-2(x-(-3))\Rightarrow y=-2x-6\Rightarrow 2x+y+6=0.$$ …

Slope value	What the line does
$m > 0$	Rises left to right (uphill)
$m < 0$	Falls left to right (downhill)
$m = 0$	Horizontal (flat)
$m$ undefined	Vertical (straight up/down)

Q.Assertion (A): Equation of a line with slope $-2$ and intersecting the $x$ axis at a distance of 3 units to the left of origin is $2x - y - 6 = 0$ .
Reason (R): Equation of a line passing through the point $(x_{1}, y_{1})$ and with slope $m$ is given by $(y - y_{1}) = m(x - x_{1})$ .

Concept understanding — Slope Calculation

Slope Calculation — From Intuition to Precision

The Intuition: Rise Over Run

The Precise Definition

What the Number Tells You

A Worked Example

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