Find the equation of the line. A line that is parallel to the graph of 2x+3y=5 and contains the point (3,1)

2x + 3y = 6

Step-by-step explanation:

The equation of a line in slope- intercept fprm is

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

Given

2x + 3y = 5 ( subtract 2x from both sides )

3y = - 2x + 5 ( divide terms by 3 )

y = - x + ← in slope- intercept form

with slope m = -

Parallel lines have equal slopes, then

y = - x + c ← is the partial equation

To find c substitute (3, 1 ) into the partial equation

1 = - 2 + c ⇒ c = 1 + 2 = 3

y = - x + 3 ( multiply through by 3 to clear the fraction )

3y = - 2x + 6 ( add 2x to both sides )

2x + 3y = 6 ← equation of parallel line

answer:  

123455421

step-by-step explanation: easy