Question

“ write the equation of the line that goes through the point (6,3) and is parallel to y=-2/3x+5 “ ????

Answer 1

see explanation

Explanation:

The equation of a line in slope- intercept form is

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

y = -
`(2)/(3)` x + 5 ← is in slope- intercept form

with slope m = -
`(2)/(3)`

Parallel lines have equal slopes, thus

y = -
`(2)/(3)` x + c ← is the partial equation of the line

To find c substitute (6, 3) into the partial equation

3 = - 4 + c ⇒ c = 3 + 4 = 7

y = -
`(2)/(3)` x + 7 ← equation of line