Question

If the equations `x + 5y = 7 and 2x + 6y = 10` are represented on a graph, what is the relationship between these lines?

Answer 1

They are two intersecting lines.

Explanation:

Two lines are either parallel or incident (or at least this is what can be graphically interesting about a couple of lines). They are parallel if and only if they have the same slope `m`, which is computed as the opposite ratio between the `x` and `y` coefficient in the implicit form `ax+by+c=0`, i.e. `-a/b`.

• First line: `x+5y-7=0`, thus the slope is `-1/5`
• Second line: `2x+6y=10`, thus the slope is `-1/3`

You can see that the lines do intersect: WolframAlpha Link