Question

Find the equation of the line which intersects the x -axis at a distance of 3 units to the left of origin with slope –2.

Answer 1

The line intersects the x-axis at a distance of three units towards left of origin and the slope of the line is −2.

Since the left side of origin lies on x-axis with negative coordinates. The point of intersection is given by ( −3,0 ).

The formula for the equation of a non-vertical line having slope m and passing through the point ( x 0 , y 0 ) is given by,

( y− y 0 )=m( x− x 0 )(1)

Substitute the values of ( x 0 , y 0 ) as ( −3,0 ) and slope m as −2 in equation (1).

( y−0 )=−2⋅( x−( −3 ) ) y=−2( x+3 ) y=−2x−6 2x+y+6=0

Thus, the equation of line intersects at a distance of three units towards left of origin and slope of −2 is 2x+y+6=0.