Find the equation of the line which passes through the point (-4, 3) with slope \(\frac 12\).

Question

If the components of \( \vec{a} = \alpha \hat{i} + \beta \hat{j} + \gamma \hat{k} \) along and perpendicular to \( \vec{b} = 3\hat{i} + \hat{j} - \hat{k} \) respectively are \( \frac{16}{11} (3\hat{i} + \hat{j} - \hat{k}) \) and \( \frac{1}{11} (-4\hat{i} - 5\hat{j} - 17\hat{k}) \), then \( \alpha^2 + \beta^2 + \gamma^2 \) is equal to:

Answer 1

Given:

The line passes through the point (−4, 3)
Slope of the line = 1/2

Step 1: Use point–slope form of a line

Equation of a line:

y − y₁ = m(x − x₁)

Substitute (x₁, y₁) = (−4, 3) and m = 1/2

y − 3 = (1/2)(x + 4)

Step 2: Simplify

y − 3 = x/2 + 2

y = x/2 + 5

Final Answer:

The equation of the required line is:
y = x/2 + 5

Find the equation of the line which passes through the point (-4, 3) with slope \(\frac 12\).

Solution and Explanation

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