Question

2) Find the equation of the straight line passing through (-2, 3) and inclined at an angle of 45 with the x- axis​

Answer 1

Answer:

x - y + 5= 0

Step-by-step explanation:

Slope of the line(m) = tanα = tan45° = 1

A point on the line is (-2, 3) = (x₁ , y₁)

       Hence the equation of the line is:

⇒ y - y₁ = m(x - x₁)

⇒ y - (3) = 1(x - (-2))

⇒ y - 3 = x + 2

⇒ x - y + 5 = 0

  Required equation is x - y + 5 = 0

Answer 2

⚘ Question :-

• Find the equation of the straight line passing through (-2, 3) and inclined at an angle of 45° with the x- axis.

⚘ Answer :-

• Required equation is x - y + 5 = 0.

✧ Explanation ✧

⚘ Given :-

• Straight line passing through (-2, 3)
• Inclined at an angle of 45° with the x- axis

⚘ To Find :-

• Equation of the straight line?

⚘ Solution :-

★ Finding slope of line ::

➨ Slope of line (m) = tanθ

➨ Slope of line (m) = tan45°

➨ Slope of line (m) = 1 $\bf \Big[\because tan45^{\circ} = 1\Big]$

Now,

★ Finding eqⁿ of the straight line ::

We know that,

$\leadsto\:{\large{\boxed{\bf{\red{m = \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}}}}}}$

Let,

• $\sf y_{2}$ be y
• $\sf x_{2}$ be x

We have,

• m = 1
• $\sf y_{2}$ = y
• $\sf y_{1}$ = 3
• $\sf x_{2}$ = x
• $\sf x_{1}$ = -2

By plugging all values in formula we get,

➨ $\tt 1 = \dfrac{y - 3}{x - (-2)}$

➨ $\tt 1 = \dfrac{y - 3}{x + 2}$

➨ $\tt 1(x + 2) = y - 3$

➨ $\tt x + 2 = y - 3$

➨ $\tt x + 2 - (y - 3) = 0$

➨ $\tt x + 2 - y + 3 = 0$

➨ $\tt x - y + 2 + 3 = 0$

➨ $\large{\underline{\underline{\bf{\purple{x - y + 5 = 0}}}}}$

∴ Eqⁿ of straight line is x - y + 5 = 0.

⚘ Know More :-

Important Formulae:

• For finding distance between two points we use distance formula i.e, $\sf \sqrt{\Big(x_{2} - x_{1}\Big)^2 + \Big(y_{2} - y_{1}\Big)^2}$
• For finding a ratio in which line segment is divided by a point we use section formula i.e, $\sf \bigg(\dfrac{m_{1}x_{2} + m_{2}x_{1}}{m_{1} + m_{2}},\:\dfrac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}}\bigg)$

⚘ Learn More on Brainly :-

Question:

• If the slope of the line passing through the point (2,5) and (-4,k) is 3/2, then the value of k is

Answer:

• brainly.in/question/41369991

★═══════════════════════★