A straight line passes through the point A(3, | vedclass

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(B) Let the line intersect the $x$-axis at $Q(a, 0)$ and the $y$-axis at $P(0, b)$.Since the point $A(3, 4)$ bisects the intercept $PQ$,it is the midp

Vedclass · Accepted Answer

$4x + 3y = 24$

Vedclass · Answer

(B) Let the line intersect the $x$-axis at $Q(a, 0)$ and the $y$-axis at $P(0, b)$.Since the point $A(3, 4)$ bisects the intercept $PQ$,it is the midpoint of $PQ$.Using the midpoint formula:$\frac{a + 0}{2} = 3 \implies a = 6$$\frac{0 + b}{2} = 4 \implies b = 8$The intercept form of the equation of the line is $\frac{x}{a} + \frac{y}{b} = 1$.Substituting the values of $a$ and $b$:$\frac{x}{6} + \frac{y}{8} = 1$Multiplying by $24$ to clear the denominators:$4x + 3y = 24$

$A$ straight line passes through the point $A(3, 4)$ such that its intercept between the axes is bisected at $A$. Find its equation.

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