Question

Given a the line y=2.5x+4, find line whose graph:
is parallel to the graph of the given line.

Answer 1

y=2.5x+10

Explanation:

The given line is y=2.5x+4.

Here, the slope of the line,
`m_0=2.5` and

the y-intercept of the line,
`C_0=4`.

The graph of the line has been shown in the figure.

The parallel lines never intersect each-other and always have a fixed distance between then.

Mathematically, a line having the slope, m, and the y-intercept, C, i.e

y=mx+C is parallel to the given line if it has equal slopes,
`m=m_0`, and different intercepts,
`C\\eq C_0`.

So, the equation of the parallel line is

y=2.5x+C, where
`C\\eq 4`.

For example, take C=10 than the equation of a parallel line is

y=2.5x+10 has been shown in the graph.

Like this, there are infinitely many possible parallel lines to the given line.