Question

What is the equation of the line that passes through (-2, 3) and is parallel to 2x + 3y = 8?

Answer 1

Slope intercept form: y= mx +b

Parallel lines= same slope

Find slope of this line first:
2x + 3y =8

Subtract 2x from left side and add it to right side.

3y = -2x + 8

Divide by 3

Y= -2x/3 +8/3

slope= -2x/3

Y= mx + b —-} b is y intercept which is unknown and m is slope

Plug in -2/3x for slope.

Y= -2/3x +b

To find y intercept plug in point (-2, 3)

Y= -2/3x+b
3= -2/3(-2) +b
3 = 4/3+b

3-4/3 =b
5/3 =b

Y= -2/3x +5/3 is new equation