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:

$y = \frac{-2}{9}x -\frac{62}{9}$

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:

$y = \frac{-2x}{9} -1$

On comparing the above equation with eqn 1,

$m = \frac{-2}{9}$

We know that slopes of parallel lines are equal

Thus slope of line parallel to given line is also $\frac{-2}{9}$

Now find the equation of line with slope $\frac{-2}{9}$ and passing through (-4, -6)

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

$\text{Substitute } m = \frac{-2}{9} \text{ and } c = \frac{-62}{9} \text{ in eqn 1}\\\\y = \frac{-2}{9}x -\frac{62}{9}$

Thus the equation of line is found