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If line 3x-ay-1=0 is parallel to the lin...

If line `3x-ay-1=0` is parallel to the line `(a+2)x-y+3=0` then find the values of a.

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To find the values of \( a \) such that the line \( 3x - ay - 1 = 0 \) is parallel to the line \( (a + 2)x - y + 3 = 0 \), we can follow these steps: ### Step 1: Convert both line equations to slope-intercept form We need to express both equations in the form \( y = mx + c \), where \( m \) is the slope. **For the first line:** Starting with the equation: \[ 3x - ay - 1 = 0 \] ...
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Knowledge Check

  • If the line y+2x+3=0 is parallel to the line 2y-px-4=0 , what is the value of p ?

    A
    `-4`
    B
    `-2`
    C
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    D
    4

  • Which of the following is an equation of the line that is parallel to the line y-4x=0 and has the same y-intercept as line y+3=x+1 ?

    A
    `y=4x-2`
    B
    `y=4x+1`
    C
    `y=-(1)/(4)x+1`
    D
    `y=-(1)/(4)x-2`

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    Let the equation of the plane containing the line x-y - z -4=0=x+y+ 2z-4 and is parallel to the line of intersection of the planes 2x + 3y +z=1 and x + 3y + 2z = 2 be x + Ay + Bz + C=0 Compute the value of |A+B+C| .

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    Find equation of the line parallel to the line 3x - 4y + 2 = 0 and passing through the point (2, 3) .

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