Algebra 1
Name: ___________________________________
Sections 4.1-4.3
Writing linear equations in slope-intercept and point-slope form
Quiz review
1. Write an equation in slope-intercept form for the line shown.
a.
b.
2. Write an equation in slope-intercept form of the line that passes through the points
a. (0,  8) and (6,  3)
b. (3, 4) and (3,  3)
3. Write an equation in slope-intercept form of the linear function f with the values
a. f (5)  4 and f (4)  2
b. f (2)  3 and f (5)  5
4. Write an equation that represents the linear function shown in the table or mapping diagram.
a.
b.
x
f(x)
–8
–2
–4
–1
4
1
For each of the following, (a) write an equation in point-slope form of the line that passes
through the given point and has the given slope and (b) rewrite the equation in slope-intercept
form.
5. (4,  5); m  6
6. (8, 2); m  
3
4
For each of the following, (a) write an equation in point-slope form of the line that passes
through the two points and (b) rewrite the equation in slope-intercept form.
7. (4, 7) and (5, 1)
8. (3,  8) and (7,  2)
For Problems 9-12, graph the equation by (1) identifying the slope and the point that was used to
write the equation, (2) plotting the point and using the slope to find a second point, and
(3) using the two points to draw the line.
9..
13.
10.
12.
11.
14.
15.
For Part (a) of Problems 16-18, (1) state the variables, including units; (2) determine the given
information (slope, y-intercept, one point, two points?), including units; (3) if needed, find the
missing slope and/or y-intercept, including units; and (4) write the equation in slope-intercept
form.
16. Rufus has collected 100 pounds of aluminum cans to recycle. He plans to collect an
additional 25 pounds each week.
a. Write a linear equation in slope-intercept form to model the situation.
b. In how many weeks will Rufus have a total of 400 pounds of cans?
17. A canoe rental service charges a transportation fee and $8 dollars an hour to rent a canoe.
Mary and Joe rented a canoe for 6 hours, and the total cost for was $68.
a. Write a linear equation in point-slope form to model the situation.
b. Rewrite the equation in slope-intercept form.
c. What is the transportation fee?
d. What is the cost of renting the canoe for 4 hours?
18. An attorney charges a fixed fee for an initial meeting and an hourly fee for all hours worked
after this meeting. The attorney charges $850 for an initial meeting and 4 hours of
additional work. S/he charges $1750 for an initial meeting and 10 hours of additional work.
a. Write a linear equation in point-slope form to model the situation.
b. Rewrite the equation in slope-intercept form.
c. What is the fee for the initial meeting? What is the hourly fee?
d. If the attorney charges a client $2350, how long did the attorney work after the initial
meeting?
Answers:
1. a. y  5 x  5 , b. y  3 x  8 ;
5
7
1
2. a. y  x  8 , b. y   x 
6
6
2
2
5
3. a. f ( x)  2 x  6 , b. f ( x)   x 
3
3
1
4. a. y  x  6 , b. y  x
4
5. a. y  5  6( x  4) , b. y  6 x  29
3
3
6. a. y  2   ( x  8) , b. y   x  4
4
4
7. a. y  7  6( x  4) or y  1  6( x  5) , b. y  6 x  31
3
3
3
25
8. a. y  8  ( x  3) or y  2  ( x  7) , b. y  x 
2
2
2
2
9. m  3, (2,  4) ;
10. m  2, (2,  3) ;
11. m  3, ( 6, 1) ;
5
12. m   , (3,  4)
2
1
1
13. y  3   ( x  4) , 14. y  1  3( x  3) , 15. y  1  ( x  1)
4
2
16. a. x = number of weeks; y = pounds of aluminum cans; m = 25 lbs/wk; b = 100 lbs
y  25 x  100
b. Rufus will have 400 pounds of cans in 12 weeks.
17. a. x = number of hours; y = total cost, $; m = 8 $/hr;  x1 , y1  = (6 hrs, $68)
y  68  8( x  6)
b. y  8 x  20
c. The transportation fee is $20.
d. The cost of renting the canoe for 4 hours is $52.
18. a. x = number of hours; y = total cost, $;  x1 , y1  = (4 hrs, $850);  x2 , y2  = (10 hrs, $1750);
m = 150 $/hr; y  850  150( x  4) or y  1750  150( x  10)
b. y  150 x  250
c. The fee for the initial meeting is $250. The hourly fee is $150.
d. The attorney worked14 hours in addition to the initial meeting if the charge was $2350.