Answer:
36. y=x
37. x=4
38. y=3x-10
39. y=-25x+49
40. [tex]y=-\dfrac{1}{18}x-\dfrac{89}{18}[/tex]
41. y=-x+3
Step-by-step explanation:
36. Parallel lines have the same slope. The slope of the line [tex]y=x+42[/tex] is [tex]m=1,[/tex] so the equation of a parallel line is
[tex]y=x+b[/tex]
This line passes through the point (2,2), so its coordinates satisfy the equation:
[tex]2=2+b\\ \\b=0[/tex]
and the equation of the line is [tex]y=x[/tex]
37. The line [tex]x=03[/tex] is vertical ine, so parallel line is also vertical line with equation [tex]x=a.[/tex] Substitute the coordinates of the point (4,3):
[tex]4=a[/tex]
hence the equation is [tex]x=4[/tex]
38. Parallel lines have the same slope. The slope of the line [tex]y=3x+24[/tex] is [tex]m=3,[/tex] so the equation of a parallel line is
[tex]y=3x+b[/tex]
This line passes through the point (2,-4), so its coordinates satisfy the equation:
[tex]-4=3\cdot 2+b\\ \\b=-10[/tex]
and the equation of the line is [tex]y=3x-10[/tex]
39. Parallel lines have the same slope. The slope of the line [tex]y=-25x+35[/tex] is [tex]m=-25,[/tex] so the equation of a parallel line is
[tex]y=-25x+b[/tex]
This line passes through the point (2,-1), so its coordinates satisfy the equation:
[tex]-1=-25\cdot 2+b\\ \\b=49[/tex]
and the equation of the line is [tex]y=-25x+49[/tex]
40. Perpendicular lines have slopes satisfying [tex]m_1\cdot m_2=-1[/tex] Since the line [tex]y=18x+26[/tex] has the slope [tex]m_1=18,[/tex] perpendicular line has the slope [tex]m_2 =-\dfrac{1}{18}.[/tex]
The equation is
[tex]y=-\dfrac{1}{18}x+b[/tex]
This line passes through the point (1,-5), so its coordinates satisfy the equation:
[tex]-5=-\dfrac{1}{18}\cdot 1+b\\ \\b=-5+\dfrac{1}{18}=-\dfrac{89}{18}[/tex]
and the equation of the line is [tex]y=-\dfrac{1}{18}x-\dfrac{89}{18}[/tex]
41. Perpendicular lines have slopes satisfying [tex]m_1\cdot m_2=-1[/tex] Since the line [tex]y=x+2[/tex] has the slope [tex]m_1=1,[/tex] perpendicular line has the slope [tex]m_2 =-1.[/tex]
The equation is
[tex]y=-x+b[/tex]
This line passes through the point (4,-1), so its coordinates satisfy the equation:
[tex]-1=-4+b\\ \\b=3[/tex]
and the equation of the line is [tex]y=-x+3[/tex]
