Question : What is the equation of the line whose y-intercept is 4 and is making an angle of 45° with the positive x-axis?
Option 1: $x+y=–4$
Option 2: $x–y=4$
Option 3: $x+y=4$
Option 4: $x–y= – 4$
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Correct Answer: $x–y= – 4$
Solution : Given: The line whose y-intercept is 4 and its making angle of 45° with the positive x-axis. Slope of the line, $m = \tan 45°=1$ By using the slope and y-intercept of the line, Slope intercept form, $y=mx+c$ $⇒y=(1)x+4$ $⇒x-y=- 4$ This is the equation of the line. Hence, the correct answer is $x-y=-4$.
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Question : The graph of the equation $x=a(a \neq 0)$ is a_____.
Option 1: line parallel to the x-axis
Option 2: line parallel to the y-axis
Option 3: line at an angle of 45 degree to y-axis
Option 4: line at an angle of 45 degree to x-axis
Question : If $\cos x=\sin y$ and $\cot(x–40°)=\tan(50°–y)$, then the values of $x$ and $y$ are:
Option 1: $x=70°,y=2°$
Option 2: $x=75°,y=15°$
Option 3: $x=85°,y=5°$
Option 4: $x=80°,y=10°$
Question : If $\sin17°=\frac{x}{y}$, then the value of $(\sec17°–\sin73°)$ is:
Option 1: $\frac{y^{2}}{x\sqrt{y^{2}–x^{2}}}$
Option 2: $\frac{x^{2}}{y\sqrt{y^{2}–x^{2}}}$
Option 3: $\frac{x^{2}}{y\sqrt{x^{2}–y^{2}}}$
Option 4: $\frac{y^{2}}{x\sqrt{x^{2}–y^{2}}}$
Question : Find the coordinates of the points where the graph $57x – 19y = 399$ cuts the coordinate axes.
Option 1: x-axis at(–7, 0) and y-axis at (0, –21)
Option 2: x-axis at(–7, 0) and y-axis at (0, 21)
Option 3: x-axis at (7, 0) and y-axis at (0, –21)
Option 4: x-axis at (7, 0) and y-axis at (0, 21)
Question : At what point does the line $3x+y=-6$ intercept the x-axis?
Option 1: (2, 0)
Option 2: (–2, 0)
Option 3: (0, –6)
Option 4: (0, 6)
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