Question

write an equation in slope intercept form for the line that passes through (4, -4) and is parallel to 3x+4x=2y-9

Answer 1

`\large\boxed{y=(7)/(2)x-18}`

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

Convert the equation of a line 3x + 4x = 2y - 9 to the slope-intercept form:

`3x+4x=2y-9`

`7x=2y-9` add 9 to both sides

`7x+9=2y` divide both sides by 2

`(7)/(2)x+(9)/(2)=y\to y=(7)/(2)x+(9)/(2)`

Parallel lines have the same slope. Therefore we have the equation:

`y=(7)/(2)x+b`

Put the coordinates of the point (4, -4) to the equation:

`-4=(7)/(2)(4)+b`

`-4=7(2)+b`

`-4=14+b` subtract 14 from both sides

`-18=b\to b=-18`

Finally we have the equation:

`y=(7)/(2)x-18`