Free Printable U2 - Systems of Equations

1.

Write an equation of a line in point slope form through the point (4, -5) and perpendicular to $y=2x+7$

(a)

2.

Write an equation of a line in slope intercept form through the point (4, -5) and perpendicular to $y=2x+7$

(a)

3.

Write an equation of a line in point slope form through the point (-6, 7) and perpendicular to $y=-3x-9$

(a)

4.

Write an equation of a line in point slope form through the point (-6, 7) and parallel to $y=-3x-9$

(a)

5.

Write an equation of a line in slope intercept form through the point (-6, 7) and perpendicular to $y=-3x-9$

(a)

6.

Write an equation of a line in point slope form through the point (-2, 7) and perpendicular to $6x+10y=30$

(a)

7.

Write an equation of a line in point slope form through the point (-2, 7) and parallel to $6x+10y=30$

(a)

8.

Write an equation of a line in point slope form through the point (5, -9) and parallel to $8x-6y=24$

(a)

9.

Write an equation of a line in point slope form through the point (5, -9) and perpendicular to $8x-6y=24$

(a)

10.

Write an equation in point slope form through the point (2, -6) and that is perpendicular to the equation.

$y=5x+9$

(a)

11.

Write an equation in point slope form through the point (-1, 2) and that is perpendicular to the equation.

$y=3x-7$

(a)

12.

Write an equation of a line in point slope form through the point (4, -5) and perpendicular to $y=2x+7$

(a)

13.

Write an equation of a line in point slope form through the point (-2, 7) and perpendicular to $6x+10y=30$

(a)

14.

Write an equation of a line in point slope form through the point (-2, 7) and parallel to $6x+10y=30$

(a)

15.

Write an equation of a line in point slope form through the point (5, -9) and parallel to $8x-6y=24$

(a)

16.

Write an equation of a line in point slope form through the point (5, -9) and perpendicular to $8x-6y=24$

(a)

17.

Match the following

a)

$y=\frac{2}{3}x-1$

$y=\frac{2}{3}x+7$

1.

Parallel Lines

b)

$y=\frac{3}{5}x-4$

$y=\frac{-5}{3}x+1$

2.

Perpendicular Lines

c)

$y=\frac{1}{4}x-3$

$y=\frac{-6}{5}x-3$

3.

Neither

18.

Match the following

a)

$y-3=\frac{4}{5}\left(x+1\right)$

$10x+8y=24$

1.

Perpendicular Lines

b)

$y-6=-\frac{3}{2}\left(x+5\right)$

$9x+6y=30$

2.

Parallel Lines

c)

$y+8=-\frac{1}{7}\left(x-3\right)$

$2x-14y=28$

3.

Neither

19.

Select all systems that have perpendicular slopes

a)

$x=2$

$y=-4$

b)

$y-1=-\frac{3}{5\ }\left(x+4\right)$ $6x-10y=20$

c)

$y=\frac{1}{4}x+7$

$8x+2y=7$

d)

$y=x-2$

$y=-x+5$

20.

Which of the following are true? Select all that apply.

a)

g(x) is perpendicular to Q(x)

b)

f(x) is parallel to Q(x)

c)

g(x) is parallel to h(x)

d)

There are no sets of parallel lines

e)

f(x) is perpendicular to h(x)

21.

Which functions are perpendicular to the given function? Select all that apply.

$12x+8y=24$

a)

$y=\frac{2}{3}x-11$

b)

$y=-\frac{3}{2}x+7$

c)

$y+4=-\frac{3}{2}\left(x-1\right)$

d)

$8x-12y=48$

e)

$y-9=\frac{2}{3}\left(x+10\right)$

22.

Which functions are parallel to the given function? Select all that apply.

$12x+8y=24$

a)

$y=\frac{2}{3}x-11$

b)

$y=-\frac{3}{2}x+7$

c)

$y+4=-\frac{3}{2}\left(x-1\right)$

d)

$6x+4y=48$

e)

$y-9=\frac{2}{3}\left(x+10\right)$

23.

Which equations are perpendicular to $2x-8y=24$ ? Select all that apply.

a)

$y=-4x+2$

b)

$y+3=-4\left(x-9\right)$

c)

$y=4x+1$

d)

$y+7=4\left(x-11\right)$

e)

$10x+5y=20$

24.

Which equations are perpendicular to $8x-2y=24$ ? Select all that apply.

a)

$y=-\frac{1}{4}x+2$

b)

$y+3=-\frac{1}{4}\left(x-9\right)$

c)

$y=\frac{1}{4}x+2$

d)

$y+7=\frac{1}{4}\left(x-11\right)$

e)

$3x+12y=36$

25.

Write an equation of a line in point-slope form that is perpendicular to the line pictured and through the point (-3, 1)

(a)

26.

Write an equation of a line in point-slope form that is perpendicular to the line pictured and through the point (4, -5)

(a)

27.

Write an equation of a line in point-slope form that is parallel to the line pictured and through the point (2, -5)

(a)

28.

Write an equation of a line in point-slope form that is parallel to the line pictured and through the point (-6, 7)

(a)

29.

What is the solution to the system with h(x) and j(x)? Write your answer as an ordered pair.

(a)

30.

Which two functions create a system with a solution in Quadrant IV?

a)

f(x)

b)

g(x)

c)

h(x)

d)

j(x)

31.

What is the solution to the system with f(x) and j(x)? Write your answer as an ordered pair.

(a)

32.

Which two functions create a system with a solution in Quadrant I?

a)

f(x)

b)

g(x)

c)

h(x)

d)

j(x)

33.

What quadrant has the solution to the system of g(x) and h(x)?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

34.

Which two functions create a system with no solution?

a)

$f\left(x\right)=\frac{2}{3}x+1$

b)

$p\left(x\right)=\frac{2}{3}x-7$

c)

$g\left(x\right)=-7x+1$

d)

$r\left(x\right)=-\frac{3}{2}x+4$

35.

Which two functions create a system with no solution?

a)

$y+4=-\frac{3}{2}\left(x-1\right)$

b)

$y=-\frac{3}{2}x+8$

c)

$y=4x+8$

d)

$6x+4y=20$

e)

$y=6x+8$

36.

Given f(x), which function would create a system of equations with no solutions?

$f\left(x\right)=-\frac{2}{3}x+4$

a)

$g\left(x\right)=-\frac{2}{3}x-5$

b)

$j\left(x\right)=\frac{3}{2}x+1$

c)

$p\left(x\right)=\frac{2}{3}x+6$

d)

$Q\left(x\right)=-\frac{3}{2}x+7$

37.

Which two functions create a system with a solution at (4, -2)?

a)

j(x)

b)

f(x)

c)

g(x)

d)

h(x)

38.

Which two functions create a system with a solution at (-1,3)?

a)

j(x)

b)

f(x)

c)

g(x)

d)

h(x)

39.

What is the solution to the system created by h(x) and j(x)? Write your answer as an ordered pair (x,y).

(a)

40.

What quadrant is the solution to the system created by f(x) and h(x)?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

41.

Select all systems that have no solutions

a)

f(x)=4x-1

g(x)=4x+3

b)

$x=2\ \ and\ \ y=3$

c)

d)

e)

j(x)=2x-3

g(x)=5x+8

42.

Select all systems that have one solution

a)

f(x)=4x-1

g(x)=4x+3

b)

$x=2\ \ and\ \ y=3$

c)

d)

e)

j(x)=2x-3

g(x)=5x+8

43.

Select all systems that have no solutions

a)

b)

c)

$f\left(x\right)=\frac{4}{5}x-7$

$g\left(x\right)=6x-7$

d)

$p\left(x\right)=\frac{-1}{3}x+2$

$Q\left(x\right)=\frac{-1}{3}x+7$

44.

Select all systems that have one solution

a)

b)

c)

$f\left(x\right)=\frac{4}{5}x-7$

$g\left(x\right)=6x-7$

d)

$p\left(x\right)=\frac{-1}{3}x+2$

$Q\left(x\right)=\frac{-1}{3}x+7$

45.