Standard Form Worksheet
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1Name: ________________________________
Period: ____
Standard Form Worksheet
COMPLETE THESE PROBLEMS NEATLY ON SERPARATE LINED PAPER and SHOW ALL STEPS!
For 1–6, write two equations in standard form that are equivalent to the given equation.
4
1
1) –7x + 8y = –4
2) 6x + 24y = 18
3) –
/
x –
/
y = 0
5
5
1
2
4) 8x – 14y = 2
5)
/
x –
/
y = –9
6) 6x + y = 1
3
3
For 7–12, write an equation in standard form of the line that passes through the given point and
has the given slope m.
3
7
7) (12, 6), m = 5
8) (–7, 8), m = –
/
9) (–2, 7), m =
/
2
5
5
5
1
10) (9, –10), m = –4
11) (
/
, –10), m = –
/
12) (–15, –4), m = –
/
2
4
3
For 13–17, write an equation in standard form of the line that passes through the given points.
13) (3, –1), (5, 7)
14) (2, 6), (3, 8)
15) (1, –16), (15, –8)
1
2
16) (7, –3), (4, 1)
17) (–4,
/
), (–6,
/
)
3
3
For 18–21, write an equation in standard form of the line that has the given values.
18) f(3) = –8 and f(5) = –9
19) g(0) = 8 and g(12) = 0
20) h(–5) = 6 and h(2) = –3
21) j(0) = –13 and j(–9) = –12
Fro 22–25, write an equation for the horizontal line that passes through the given point, and write
another equation for the vertical line that passes through the gvein point.
22) (8, 3)
23) (–9, –1)
24) (–2, 6)
25) (0, 0)
26) Your cell phone plan charges you $.02 to send a text (X) message and $.05 to receive a text (Y)
message. You promised your parents you will spend no more than $2.50 a month on text messaging.
a) Write an equation in that models the possible
combinations of sent text messages and received text
messages to total your goal of $2.50.
b) Convert your equation from part a to standard form.
c) Convert your equation from part b to slope-intercept
form.
d) Find the x- and y-intercepts of the equation. Use the
intercepts to graph the line.
f) Explain what each of these intercepts represent in terms of your messaging.
EVEN ANSWERS:
#1–6) Answers will vary. (You should multiply or divide each term by the same integer to get an equivalent equation.
However, your answer cannot have fractions or decimals in it because it said “Standard Form.
8)
3x + 2y = –5
10) 4x + y = 26
12) x + 3y = –27
14) –2x + y = 2
16)
4x + 3y = 19
18) x + 2y = –13
20) 9x + 7y = –3
22) Vertical line through (8, 3) is x = 8. Horizontal line through (8, 3) is y = 3.
24) Vertical line through (–2, 6) is x = –2. Horizontal line through (–2, 6) is y = 6.
26) a) 0.02x + 0.05y = 2.50
b) 2x + 5y = 250
2
c) y = –
/
x + 50
5
d) x-intercept: (125, 0), y-intercept: (0, 50)
e) The x-intercept (125, 0) means that one way to owe exactly $2.50 is to send 125
messages and receive none. The y-intercept (0, 50) means another way to owe
.
exactly $2.50 is to receive 50 messages and send none
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