Question

Please help! question attached

write equation parallel to a given line
write equation of a line perpendicular to a given line

Answer 1

36. y=x

37. x=4

38. y=3x-10

39. y=-25x+49

40.
`y=-(1)/(18)x-(89)/(18)`

41. y=-x+3

Explanation:

36. Parallel lines have the same slope. The slope of the line
`y=x+42` is
`m=1,` so the equation of a parallel line is

`y=x+b`

This line passes through the point (2,2), so its coordinates satisfy the equation:

`2=2+b\\ \\b=0`

and the equation of the line is
`y=x`

37. The line
`x=03` is vertical ine, so parallel line is also vertical line with equation
`x=a.` Substitute the coordinates of the point (4,3):

`4=a`

hence the equation is
`x=4`

38. Parallel lines have the same slope. The slope of the line
`y=3x+24` is
`m=3,` so the equation of a parallel line is

`y=3x+b`

This line passes through the point (2,-4), so its coordinates satisfy the equation:

`-4=3\cdot 2+b\\ \\b=-10`

and the equation of the line is
`y=3x-10`

39. Parallel lines have the same slope. The slope of the line
`y=-25x+35` is
`m=-25,` so the equation of a parallel line is

`y=-25x+b`

This line passes through the point (2,-1), so its coordinates satisfy the equation:

`-1=-25\cdot 2+b\\ \\b=49`

and the equation of the line is
`y=-25x+49`

40. Perpendicular lines have slopes satisfying
`m_1\cdot m_2=-1` Since the line
`y=18x+26` has the slope
`m_1=18,` perpendicular line has the slope
`m_2 =-(1)/(18).`

The equation is

`y=-(1)/(18)x+b`

This line passes through the point (1,-5), so its coordinates satisfy the equation:

`-5=-(1)/(18)\cdot 1+b\\ \\b=-5+(1)/(18)=-(89)/(18)`

and the equation of the line is
`y=-(1)/(18)x-(89)/(18)`

41. Perpendicular lines have slopes satisfying
`m_1\cdot m_2=-1` Since the line
`y=x+2` has the slope
`m_1=1,` perpendicular line has the slope
`m_2 =-1.`

The equation is

`y=-x+b`

This line passes through the point (4,-1), so its coordinates satisfy the equation:

`-1=-4+b\\ \\b=3`

and the equation of the line is
`y=-x+3`