Question

Write standard form of line that is parallel to 2x + 3y= 4 and passes through the point (1, -4)

Answer 1

2x + 3y = -10

Explanation:

First convert the line into slope intercept form to find the slope of the line.

2x + 3y = 4

3y = 4 - 2x

y = -2/3x + 4/3

The slope of the line is -2/3. Parallel lines have the same slope so the slope for a line through the point (1,-4) will be -2/3. Substitute m = -2/3 and (1,-4) into the point slope of a line.

`y --4 = -(2)/(3)(x-1)\\y + 4 = -(2)/(3)(x -1)`

Now convert the line into standard form by using the distributive property.

`y + 4 = -(2)/(3)(x -1)\\y + 4 = -(2)/(3)x + (2)/(3)\\3y + 12 = -2x + 2\\2x + 3y + 12 = 2\\2x + 3y = -10`