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Answer:
[tex]y = - \frac{2}{3} x + 1[/tex]
Step-by-step explanation:
2x +3y= 5
3y= -2x +5
Divide both sides by 3:
[tex]y = - \frac{2}{3} x + \frac{5}{3} [/tex]
[tex]y = - \frac{2}{3} x + 1 \frac{2}{3} [/tex]
Now that the equation is in the slope-intercept form (y= mx +c), the slope of the given line is the coefficient of x.
[tex]slope = - \frac{2}{3} [/tex]
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,
[tex] - 1 = - \frac{2}{3} (3) + c[/tex]
-1= -2 +c
c= -1 +2
c= 1
Thus, the equation of the line is y= -⅔x +1.