Two points of each line are given below write the equation of these lines
A( $-$ 3, 4) and B(4, 5).

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Solution

The given points are A( $-$ 3, 4) and B(4, 5).
Here, x₁ = $-$ 3, x₂ = 4, y₁ = 4 and y₂ = 5
Equation in two point form is given by

$\frac{x - x_{1}}{x_{1} - x_{2}} = \frac{y - y_{1}}{y_{1} - y_{2}}$

$\Rightarrow \frac{x - (- 3)}{- 3 - 4} = \frac{y - 4}{4 - 5} \Rightarrow \frac{x + 3}{- 7} = \frac{y - 4}{- 1} \Rightarrow \frac{x + 3}{7} = \frac{y - 4}{1}$
⇒ x + 3 = 7 (y $-$ 4)
⇒ x + 3 = 7y $-$ 28
∴ x $-$ 7y + 31 = 0, which is the required equation of the line.

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Question 5
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Two points of each line are given below write the equation of these lines A(-3, 4) and B(4, 5).

The given points are A(-3, 4) and B(4, 5). Here, x1 = -3, x2 = 4, y1 = 4 and y2 = 5 Equation in two point form is given by x-x1x1-x2=y-y1y1-y2 ⇒x-(-3)-3-4=y-44-5⇒ x+3-7=y-4-1⇒x+37=y-41 ⇒ x + 3 = 7 (y-4) ⇒ x + 3 = 7y - 28 ∴ x - 7y + 31 = 0, which is the required equation of the line.

Two points of each line are given below write the equation of these lines
A( $-$ 3, 4) and B(4, 5).