Find the value of $y$, if the line joining the points $(3, y)$ and $(2, 7)$ is parallel to the line joining the points $(-1, 4)$ and $(0, 6)$.

Question

Accepted Answer

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> [!TLDR]
> Set the slope of the line through $(3,y)$ and $(2,7)$ equal to the slope of the line through $(-1,4)$ and $(0,6)$.
>
> Slope of the line joining $(-1,4)$ and $(0,6)$:
> $$m = \frac{6-4}{0-(-1)} = \frac{2}{1} = 2$$
>
> Slope of the line joining $(3,y)$ and $(2,7)$: …

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.Find the value of $y$ , if the line joining the points $(3, y)$ and $(2, 7)$ is parallel to the line joining the points $(-1, 4)$ and $(0, 6)$ .

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

Q.Find the value of yyy, if the line joining the points (3,y)(3, y)(3,y) and (2,7)(2, 7)(2,7) is parallel to the line joining the points (−1,4)(-1, 4)(−1,4) and (0,6)(0, 6)(0,6).

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Q.Find the value of $y$ , if the line joining the points $(3, y)$ and $(2, 7)$ is parallel to the line joining the points $(-1, 4)$ and $(0, 6)$ .

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