Transcript Example 1 - Cloudfront.net

WARM-UP
Solve the following equations for y:
1) 2x + y = 10
2) 6x – 3y = –3
Find the value of y when x = –3
3) y = x – 7
4) y = –5x + 1
WARM-UP
Solve the following equations for y:
1) y  2 x  10
1) 2x + y = 10
2) 6x – 3y = –3
2) y  2 x  1
Find the value of y when x = –3
3) y = x – 7
3)  10
4) y = –5x + 1
4) 16
Algebra
NOTES
Verifying a point is on a line
Verifying a point is on the line
• If given a graph
– Plot the point to decide if it is on the line
– Justify your answer algebraically by
substituting the values into the equation of the
line
• If given an equation
– Substitute the values from the point into the
equation and simplify
– Decide if the equation is true
Example 1
• Use the graph to
decide whether the
point lies on the graph
of 4x + y = 8. Justify
your answer
algebraically.
a) (1, 4) Yes… but
we have to
check
Example 1
• Use the graph to
decide whether the
point lies on the graph
of 4x + y = 8. Justify
your answer
algebraically.
a) (1, 4)
(1, 4)
4x + y = 8
4(1) + 4 = 8
4+4=8
8=8
Yes, (1, 4) is on the
line
Example 1
• Use the graph to
decide whether the
point lies on the graph
of 4x + y = 8. Justify
your answer
algebraically.
b) (3, 4) No… but
we have to
check
Example 1
• Use the graph to
decide whether the
point lies on the graph
of 4x + y = 8. Justify
your answer
algebraically.
b) (3, 4)
(3, 4)
4x + y = 8
4(3) + 4 = 8
12 + 4 = 8
16 ≠ 8
No, (3, 4) is not on
the line
Example 2
•
Use the graph to
decide whether the
point lies on the
graph of x – 2y = 5.
Justify your answer
algebraically.
a) (3, –4)
b) (5, 0)
YOU TRY!
Example 2
•
Use the graph to
decide whether the
point lies on the
graph of x – 2y = 5.
Justify your answer
algebraically.
a) (3, –4) NO
b) (5, 0)
YES
YOU TRY!
Example 3
•
Decide whether the
ordered pair is a
solution to the
equation y = –2
a) (–2, 2)
b) (–2, –2)
y = –2 means that
the y value is –2
(x, y)
Only (b) has the y
value being –2
NO, 2 ≠ -2
yes, -2 ≠ -2
Hence, (–2, –2) is the
solution to y = –2
Example 4
Decide which of the two points lies on the
graph of the line.
2x + 4y = 8
(a)2(2) + 4(1) = 8
(a) (2, 1)
8 = 8 yes
(b) (1, 2)
(b)2(1) + 4(2) = 8
10≠8 no