Algebra 1 Common Core Student Edition, Grade 8-9

Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses

Practice

Q Apply

Write an equation in slope-intercept form of the line that passes through the

given point and is parallel to the graph of the given equation.

7. ( 1 ,3 );y = 3x + 2 8. (2, - 2 ) ; y = - x - 2

4b See Problem 1.

10. (2, - l ) ; y = - f * + 6 11. (0 ,0 );y = f x + 1
    9. (1, —3 );y + 2 = 4(x — 1)


11. (4,2); x = -3

Determine whether the graphs of the given equations are parallel,

perpendicular, or neither. Explain.

See Problem 2.

13. y = x + 11
    y = - x + 2


14. y — 4 = 3(x + 2)
    2x + 6y = 10
    14. y = 4 *- 1
    y = | x + 29
    17. y = - 7
    15. y = - 2 x + 3
    2x + y = 7
    18. y = 4 x - 2
    
    
    • x + 4y = 0
    
    
    
    

Write an equation in slope-intercept form of the line that passes through the

given point and is perpendicular to the graph of the given equation.

1

4fb See Problem 3.

19. (0, 0 );y = —3 x + 2


20. ( —3, 2 ) ; x — 2y = 7


21. ( —2, 3 );y = | x — 1


22. (5, 0); y + l = 2 ( x - 3 )


23. (1, —2 );y = 5x + 4


24. (1, —6); x — 2y = 4

4fb See Problem 4.

Park

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25. Urban Planning A p a th for a n ew city park will
    connect th e park entrance to M ain Street. I h e
    p a th should be p erp en d icu lar to M ain Street.
    W hat is an equ atio n th a t represents th e path?


26. Bike Path A bike p a th is being p la n n e d for
    the p ark in Exercise 25. The bike p a th will be
    parallel to M ain Street an d will pass through the
    park entrance. W hat is an eq u a tio n of th e line
    th a t represents the bike path?


27. Identify each pair of parallel lines. Then identify each pair of p erp en d icu lar lines.
    line a: y = 3x + 3 l i n e b : x = - l line c: y - 5 = | ( x - 2)
    line d: y = 3 line e: y + 4 = —2(x + 6) lin e /: 9x — 3y = 5
    Determine whether each statement is always, sometimes, or never tru e. Explain.


28. A horizontal line is parallel to the x-axis.


29. Two lines with positive slopes are parallel.


30. Two lines w ith the sam e slope an d different y-intercepts are perpendicular.


31. Reasoning For an arithm etic sequence, the first term is A (l) = 3. Each successive
    term adds 2 to th e previous term. A nother arithm etic seq u en ce has the
    rule B(ri) = 5 + {n — 1 )d, w h e re n is the term n u m b er an d d is the
    com m on difference. If the graphs of the two sequences are parallel,
    w hat is the value of dl Explain.


32. Reasoning Will th e graph of th e line re p resen te d by th e table
    intersect th e g raph of y = 4x + 5? Explain.

X -1 (^012)
y -1^3711
334 Chapter 5 Linear Funct ions