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

Answer:

$y = - \frac{2}{3} x + 1$

Step-by-step explanation:

2x +3y= 5

3y= -2x +5

Divide both sides by 3:

$y = - \frac{2}{3} x + \frac{5}{3}$

$y = - \frac{2}{3} x + 1 \frac{2}{3}$

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

$slope = - \frac{2}{3}$

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,

$- 1 = - \frac{2}{3} (3) + c$

-1= -2 +c

c= -1 +2

c= 1

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