Question

What is the equation of the line that passes through the point (5,6) and has a slope of 2?

Answer 1

Answer:

Answer is at the bottom!!

Step-by-step explanation:

y = - \frac{2}{5} x - 2

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange 2x + 5y = 10 into this form

subtract 2x from both sides  

5y = - 2x + 10 ( divide all terms by 5 )

y = - \frac{2}{5} x + 2 ← point- slope form with slope m = - \frac{2}{5}

Parallel lines have equal slopes hence  

y = - \frac{2}{5} x + c is the partial equation of the parallel line

to find c, substitute ( 5, - 4 ) into the partial equation

- 4 = - 2 + c ⇒ c = - 4 + 2 = - 2

y = - \frac{2}{5} x - 2 ← equation of parallel line

Hope this helps!!