Question

What is the y-intercept of the line that is parallel to 2x + 3y = 4 and contains the point (6, -2)?

Answer 1

the given equation is,

`2x+3y=4`

or, `y=-2/3x +4/3`

now,let the equation of the line required be `y=mx+c`,where, `m` is the slope and `c` is the intercept.

Now,for both the lines to be parallel,slopes must be the same,so we get, `m=-2/3`

So,the equation of the line becomes, `y=-2/3x+c`

Now,given that the line passes through point `(6,-2)`,so putting in the equation we get,

`-2=(-2/3)*6+c`

or, `c=2`

And the equation becomes, `y=-2/3 x+2` graph{y=-2/3x+2 [-10, 10, -5, 5]}