Question

Write the equation of a line parallel to the line 2x + 3y = 5 and passes through the point (9, -3) y = 2x – 21

Answer 1

y= -2/3x+3

Explanation:

Given line:

• 2x+3y= 5 ⇒ 3y= -2x+5 ⇒ y= -2/3x+5/3 in slope-intercept form

Parallel line has the same slope and equation is:

• y= -2/3x +b

using the given point (9, -3) we can find y-intercept:

• b= y+2/3x = -3+9*2/3= -3+6= 3

So the required equation is:

• y= -2/3x+3

Answer 2

y = -2/3x +3

Explanation:

2x + 3y = 5

First we need to find the slope of this line by subtracting 2x

3y = -2x +5

Divide by 3

3y/3 = -2/3x +5/3

y = -2/3x +5/3

The slope is -2/3

Parallel lines have the same slope

We have the point (9,-3)

y = mx+b

where m is the slope and b is the m intercept

y = -2/3x+b

-3 = -2/3(9) +b

-3 = -6+b

-3+6 = -6+6+b

3 = b

y = -2/3x +3