Question

Write the point-slope form of the line that passes through the origin and is parallel to a line with a slope of 2. include all of your work in your final answer.

Answer 1

The point-slope form of the line that passes through the origin and is parallel to a line with a slope of 2 is y = 2x

Solution:

The point slope form of the line that passes through the points
`\left(x_(1) y_(1)\right)` and parallel to the line with slope “m” is given as

`\bold{y - y_(1) = m\left(x - x_(1)\right)}` --- eqn 1

where “m” is the slope of the line and
`\left(x_(1) y_(1)\right)` are the points that passes through the line.

From question, given that slope = 2

Given that the line passes through the origin. i.e.
`\left(x_(1) y_(1)\right) = (0,0)`

By substituting the values in eqn 1, the point slope form of the given line can be found out by,

y – 0 = 2(x-0)

y = 2x

Hence the point-slope form of the line that passes through the origin and is parallel to a line with a slope of 2 is y = 2x