Question

How do you graph the line that passes through (0,3) parallel to the graph `6y-10x=30`?

Answer 1

See a solution process below..

Explanation:

Recall equation of a line;

`y = mx + c`

Where;

`m = "gradient"`

`c = "intercept"`

Now given;

`6y - 10x = 30`

`6y = 10x + 30`

`y = 10/6x + 30/6`

`y = 5/3x + 5`

Gradient `= 5/3`

Note: when two lines are parallel to each other, their gradients equals to each other and when the lines are perpendicular to eachother, the multiplication of their gradients equals `-1​`

Therefore;

Gradient of the second equation `= 5/3`

`(0,3)` let `(x,y)` be another points

`(y-3)/(x-0) = 5/3`

Cross multiplying..

`3y - 9 = 5x - 0`

`3y = 5x + 9`

`3y - 5x - 9 = 0`