Question

Question #cedd2

Answer 1

Equation of the line passing through point (-4, -4) is
**
`color(violet)(2y - x + 4 = 0)`

Explanation:

Equation of a line, given Slope ‘m’ is `color(red)(y = mx + c)`

Given equation is
`2y - x = 6`
`2y = x + 6`

`y = (1/2)(x + 6) = (1/2)x + 3`

`:. color(purple)(m = (1/2))`

Since the line passing through point (-4, -4) is parallel to the above line,
Slope of this line is also m and is = (1/2)

Standard form of equation through a point knowing slope is
`color(brown)((y-y_1) = m * (x - x_1))`

`(y-(-4)) = (1/2) (x - (-4)`

`(y+4) = (1/2) (x + 4)`

`2y + 8 = x + 4`

`color(green)(2y - x + 4 = 0)`

Answer 2

The equation of the line would be `y=x/2 -2`.

Explanation:

Firstly, find the slope of the line:
The line is parallel to `2y - x =-6`
We can rearrange the line into slope-intercept form.
`2y-x=-6`
`2y-x+x=-6+x`
`2y =x-6`
`y =x/2-3`

Since parallel lines have the same slope, the slope of our line would be `1/2`.

Secondly, find the y-intercept:
Our line is now in the form `y=x/2 + b`
We have the point `(x,y) = (-4,-4)`, which we can substitute into the equation.
`y=x/2 + b`
`-4=(-4)/2 + b`
`-4=-2 + b`
`b=-2`

Therefore, the equation of the line would be `y=x/2 -2`.