For what values of a and b are the intercepts | vedclass

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Question

(D) The equation of the line $ax + by + 8 = 0$ can be written in intercept form as $\frac{x}{-8/a} + \frac{y}{-8/b} = 1$. The equation of the line $2x

Vedclass · Accepted Answer

$a = -\frac{8}{3}, b = 4$

Vedclass · Answer

(D) The equation of the line $ax + by + 8 = 0$ can be written in intercept form as $\frac{x}{-8/a} + \frac{y}{-8/b} = 1$. The equation of the line $2x - 3y + 6 = 0$ can be written as $2x - 3y = -6$,which simplifies to $\frac{x}{-3} + \frac{y}{2} = 1$. According to the problem,the intercepts of the first line are equal in length but opposite in sign to the intercepts of the second line. Therefore,$-\frac{8}{a} = -(-3) = 3 \Rightarrow a = -\frac{8}{3}$. And $-\frac{8}{b} = -(2) = -2 \Rightarrow b = 4$.

For what values of $a$ and $b$ are the intercepts cut off on the coordinate axes by the line $ax + by + 8 = 0$ equal in length but opposite in sign to those cut off by the line $2x - 3y + 6 = 0$ on the axes?

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