Q.Find equation of the line through the point $(0, 2)$ making an angle $\frac{2\pi}{3}$ with the positive $x$ axis. Also find the equation of line parallel to it and crossing the $y$ axis at a distance of 2 units below the origin.

Showing the 12 most recent of 21 on this concept.

1. CBSE 2026Set ANNUAL1 markMCQ
   Q.Slope of the line which makes an angle of $30°$ with the positive direction of $y$-axis measured anticlockwise is

   (a) $-\sqrt{3}$

   (b) $-\dfrac{1}{\sqrt{3}}$

   (c) $\dfrac{1}{\sqrt{3}}$

   (d) $\sqrt{3}$

   ›Reveal solutionSolution

   Convert the angle measured from the $y$-axis to the equivalent angle measured (anticlockwise) from the $x$-axis, then take its tangent as the slope.

   Slope is defined as $\tan\theta$ where $\theta$ is the angle the line makes with the positive $x$-axis, measured anticlockwise. The positive $y$-axis itself is at $90°$ from the positive $x$-axis. If the line makes a further $30°$ with the positive $y$-axis (measured anticlockwise, i.e. swinging past the …

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2. CBSE 2026Set ANNUAL1 markMCQ
   Q.The slope of any line parallel to X-axis is:

   (a) $0$

   (b) $1$

   (c) $-1$

   (d) Not defined.

   ›Reveal solutionSolution

   A line parallel to the X-axis is horizontal, so its slope $m=\tan\theta$ with $\theta=0°$, giving $m=0$.

   …

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3. CBSE 2026Set ANNUAL1 markMCQ
   Q.The slope of x-axis is:

   (a) $90^\circ$

   (b) 1

   (c) 0

   (d) $45^\circ$

   ›Reveal solutionSolution

   Slope of a line $= \tan\theta$, where $\theta$ is the angle it makes with the positive x-axis; the x-axis itself makes a $0^\circ$ angle with itself.

   …

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4. CBSE 2026Set 1A1 mark
   Q.Find the equation of the line which is passing through the point $(-4, 3)$ with slope $\frac{1}{2}$.

   ›Reveal solutionSolution

   Point-slope form through $(-4,3)$ with slope $\tfrac12$ gives $x-2y+10=0$.

   Using $y-y_1=m(x-x_1)$ with $(x_1,y_1)=(-4,3)$ and $m=\tfrac12$: …

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5. CBSE 2025Set ANNUAL1 markMCQ
   Q.The slope of the line passing through the points $(3, -2)$ and $(7, -2)$ is

   (a) 0

   (b) 1

   (c) 4

   (d) -1

   ›Reveal solutionSolution

   The slope is $0$ — the line through these points is horizontal.

   The slope formula is $m = \dfrac{y_2-y_1}{x_2-x_1}$.

   For $(3,-2)$ and $(7,-2)$: $m = \dfrac{-2-(-2)}{7-3} = \dfrac{0}{4} = 0$.

   …

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6. CBSE 2025Set ANNUAL1 mark
   Q.The slope of the line 3x − 4y + 10 = 0 is 4/3. (True/False)

   ›Reveal solutionSolution

   Writing the line in slope-intercept form gives the true slope, which does not match the statement.

   Line: $3x - 4y + 10 = 0$

   Solve for $y$: $4y = 3x+10 \Rightarrow y = \dfrac{3}{4}x + \dfrac{10}{4}$

   …

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7. CBSE 2025Set ANNUAL1 mark
   Q.Fill in the blank: The slope of the line $6x + 3y - 5 = 0$ will be ____.

   ›Reveal solutionSolution

   Rearranging $6x + 3y - 5 = 0$ into $y = mx + c$ form shows the slope $m = -2$.

   Starting from $6x + 3y - 5 = 0$, solve for $y$:

   $3y = -6x + 5$

   $y = -2x + \dfrac{5}{3}$

   …

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8. CBSE 2025Set ANNUAL1 mark
   Q.Find the slope of the line passing through the points $(3, -2)$ and $(-1, 4)$.

   ›Reveal solutionSolution

   Using the two-point slope formula on $(3,-2)$ and $(-1,4)$ gives slope $-\dfrac{3}{2}$.

   Slope $m = \dfrac{y_2 - y_1}{x_2 - x_1}$.

   With $(x_1,y_1) = (3,-2)$ and $(x_2,y_2) = (-1,4)$:

   …

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9. CBSE 2024Set ANNUAL1 markMCQ
   Q.A line makes an angle of $30^\circ$ with the positive direction of x-axis. Find the slope of the line —

   (a) $\dfrac{\sqrt{3}}{2}$

   (b) $\sqrt{3}$

   (c) $\dfrac{1}{\sqrt{3}}$

   (d) $\dfrac{2}{\sqrt{3}}$

   ›Reveal solutionSolution

   The slope is $\tan30^\circ=\dfrac{1}{\sqrt3}$.

   …

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10. CBSE 2024Set ANNUAL1 markMCQ
    Q.The slope of a line passing through the points $(3, -2)$ and $(7, -2)$ is:

    (a) $0$

    (b) $1$

    (c) $-1$

    (d) Not defined.

    ›Reveal solutionSolution

    The slope of the line through $(3,-2)$ and $(7,-2)$ is $0$.

    Slope formula: $m=\dfrac{y_2-y_1}{x_2-x_1}$. With $(x_1,y_1)=(3,-2)$ and $(x_2,y_2)=(7,-2)$:

    $m=\dfrac{-2-(-2)}{7-3}=\dfrac{0}{4}=0.$ …

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11. CBSE 2024Set ANNUAL1 mark
    Q.Fill in the blank: The slope of the line $4x + y + 5 = 0$ is ______.

    ›Reveal solutionSolution

    Rearranging $4x+y+5=0$ into $y=mx+c$ form shows the slope is $-4$.

    Step 1. Rearrange: $y = -4x - 5$.

    …

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12. CBSE 2024Set ANNUAL1 mark
    Q.Write the slope of a horizontal line.

    ›Reveal solutionSolution

    A horizontal line has $y$ constant, so its slope (rate of change of $y$ with $x$) is 0.

    Step 1. A horizontal line has the form $y = c$ for a constant $c$.

    …

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