Find an equation of the line that passes through the given point and is parallel to the given line. Write the equation in slope-intercept form

Question

Find an equation of the line that passes through the given point and is parallel to the given line. Write the equation in slope-intercept form.

Answer 1

We don't necessarily need specific points. we can assume that the given points are x₀ and y₀

if the equation of the line is y = mx + b then the equation of a line that is parallel to this will be y = mx + b₁ where b doesn't equal b₁ and m = m

Using point slop form:

y - y₀ = m(x-x₀)

after some trivial algebra

y = mx - mx₀ + y₀ ( where b = -mx₀ + y₀ also known as y-intercept)

Answer 2

Philip is correct, but perhaps I can give some additional help.

If the equation of the line is y = mx +b

and the point is (x₀,y₀)

then the equation of the parallel line is m = (y - y₀)/(x - x₀)