Question

What is the equation of the line the passes through the point `(0, 2)` and is parallel to `6y=5x-24`?

Answer 1

The equation of the line passing through `(0,2)` is `6y=5x+12`.

Explanation:

Parallel lines have equal slopes.
The slope of the line `6y=5x-24 or y= 5/6*x-4` is `5/6`

So the slope of the line passing through `(0,2)` is also `5/6`

The equation of the line passing through `(0,2)` is `y-2=5/6*(x-0) or y-2 = 5/6 x or 6y-12=5x or 6y=5x+12` [Ans]

Answer 2

`y = 5/6x +2`

Explanation:

The first thing you should notice is that the point `color(red)((0,2)`
is a specific point on the line.

The `x` value = 0, tells us that the point is on the y-axis.

In fact it is `c " "rarr` the y-intercept.

Parallel lines have the same slope.

`6y = 5x-24` can be changed to

`y = color(blue)(5/6)x -4" "larr m = color(blue)(5/6)`

The equation of a line can be written in the form `y =color(blue)(m)x + color(red)(c)`

We have both m and c, substitute them into the equation.

`y =color(blue)(5/6)x + color(red)(2)`