Question

find an equation of the line passing through the point (-4,-6) that is parellel to the line y=-2/9x-1

Answer 1

The equation of the line passing through the point (-4,-6) in slope intercept form is:

`y = (-2)/(9)x -(62)/(9)`

Solution:

Given that we have to write the equation of the line passing through the point (-4,-6) that is parallel to the line y=-2/9x-1

The equation of line in slope intercept form is given as:

y = mx + c ---------- eqn 1

Where, "m" is the slope of line and "c" is the y intercept

Given equation of line is:

`y = (-2x)/(9) -1`

On comparing the above equation with eqn 1,

`m = (-2)/(9)`

We know that slopes of parallel lines are equal

Thus slope of line parallel to given line is also
`(-2)/(9)`

Now find the equation of line with slope
`(-2)/(9)` and passing through (-4, -6)

`\text{Substitute } m = (-2)/(9) \text{ and } (x, y) = (-4, -6) \text{ in eqn 1}\\\\-6=(-2)/(9) * -4+c\\\\-6 = (8)/(9)+c\\\\-6 = (8+9c)/(9)\\\\-54 = 8+9c\\\\9c = -62\\\\c = (-62)/(9)`

`\text{Substitute } m = (-2)/(9) \text{ and } c = (-62)/(9) \text{ in eqn 1}\\\\y = (-2)/(9)x -(62)/(9)`

Thus the equation of line is found