### Compare the general form of equation of two straight lines

Question Sample Titled 'Compare the general form of equation of two straight lines'

In the figure, the equations of the straight lines ${L}_{{1}}$ and ${L}_{{2}}$ are ${a}{x}+{y}={b}$ and ${c}{x}+{y}={d}$ respectively. Which of the following are true?

 I. ${a}$ $<{0}$ II. ${a}$ $<{c}$ III. ${b}$ $>{d}$ IV. ${a}{d}$ $>{b}{c}$

${x}$${y}$${L}_{{1}}$${L}_{{2}}$
A
I, II and III only
B
I, II and IV only
C
I, III and IV only
D
II, III and IV only

 ${a}{x}+{y}={b}$ $\ldots{L}_{{1}}$ ${c}{x}+{y}={d}$ $\ldots{L}_{{2}}$ ${y}=-{a}{x}+{b}$ $\ldots{L}_{{1}}$ ${y}=-{c}{x}+{d}$ $\ldots{L}_{{2}}$ The slopes of ${L}_{{1}}$and ${L}_{{2}}$ are $-{a}$ and $-{c}$ respectively. The y-intercepts of ${L}_{{1}}$and ${L}_{{2}}$ are ${b}$ and ${d}$ respectively. The x-intercepts of ${L}_{{1}}$and ${L}_{{2}}$ are $\dfrac{{b}}{{a}}$ and $\dfrac{{d}}{{c}}$ respectively. I. From the figure, the slope of ${L}_{{1}}$ is positive, i.e., $-{a}>{0}$ ∴  ${a}<{0}$ II. From the figure, the slope of ${L}_{{1}}$ is more positive than that of ${L}_{{2}},$i.e., $-{a}>-{c}$ ∴  ${a}<{c}$ III. From the figure, the y-intercept of ${L}_{{1}}$is larger than that of ${L}_{{2}}.$ ∴  ${b}>{d}$ IV. From the figure, the x-intercept of ${L}_{{1}}$is larger than that of ${L}_{{2}}.$ ∴  $\dfrac{{b}}{{a}}>\dfrac{{d}}{{c}}$ ${b}{c}>{a}{d}$ both ${a}<{0}$ and ${c}<{0}$ ${a}{d}<{b}{c}$

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