Question

Find equation of line a line that is parellel to the graph of 2x+3y=5 and contains the point (3,-1)

Answer 1

`y = - (2)/(3) x + 1`

Explanation:

2x +3y= 5

3y= -2x +5

Divide both sides by 3:

`y = - (2)/(3) x + (5)/(3)`

`y = - (2)/(3) x + 1 (2)/(3)`

Now that the equation is in the slope-intercept form (y= mx +c), the slope of the given line is the coefficient of x.

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

Parallel lines have the same slope.

Slope of unknown line= -⅔

y= -⅔ +c

To find the value of c, substitute a pair of coordinates into the equation.

When x= 3, y= -1,

`- 1 = - (2)/(3) (3) + c`

-1= -2 +c

c= -1 +2

c= 1

Thus, the equation of the line is y= -⅔x +1.