### Straight Line on Coordinate Plane

Question Sample Titled 'Straight Line on Coordinate Plane'

 Which of the following descriptions about the straight line ${L}:{2}{x}+{7}{y}={0}$ are true? I. ${L}$ is parallel to the straight line ${8}{x}+{28}{y}+{2}={0}.$ II. ${L}$ is perpendicular to the straight line ${7}{x}+{2}{y}={0}.$ III. ${L}$ passes through the origin. IV. The ${x}$ -intercept of ${L}$ is ${2}$ and the ${y}$ -intercept of ${L}$ is ${7}.$

A
I and III only
B
II and III only
C
II and IV only
D
I, II, III and IV

 Slope of ${L}=-\dfrac{{2}}{{7}}$ (I) Slope of straight line ${8}{x}+{28}{y}+{2}={0}$ is $-\dfrac{{8}}{{28}}=-\dfrac{{2}}{{7}}$ ∴   They are parallel to each other. (II) Slope of straight line ${7}{x}+{2}{y}={0}$ is $-\dfrac{{7}}{{2}}$ Slope of ${L}\times$(Slope of straight line ${7}{x}+{2}{y}={0}$ ) $={\left(-\dfrac{{2}}{{7}}\right)}\times{\left(-\dfrac{{7}}{{2}}\right)}$ $={1}\ne-{1}$ ∴   They are not perpendicular to each other. (III) Subsititute ${x}={0}$ and ${y}={0}$ into ${L}$ L.H.S. $={2}{\left({0}\right)}+{7}{\left({0}\right)}$ $={0}$ $=$ R.H.S. ∴  ${L}$ passes through the origin. (IV) ${L}$ passes through the origin. ∴  ${x}$ -intercept$={y}$ -intercept$={0}$

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