Algebra
Verifying a point is on the
line
If given a graph
UNIT 6
* Verifying a point on a line &
* Slope Given Two Points
Plot the point and see 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
Example 1
Use the graph to
decide whether the
point lies on the graph
of 4x + y = 8.
8. Justify
your answer
algebraically.
Use the graph to
decide whether the
point lies on the graph
of 4x + y = 8.
8. Justify
your answer
algebraically.
a) (1, 4) Yes but
a) (1
(1, 4)
we have to
check
(1, 4)
4x + y = 8
4(1) + 4 = 8
4+4=8
8=8
Yes, (1, 4) is on the
line
(3, -4)
Example 2
Use the graph to
decide whether the
point lies on the
graph of x – 2y = 5.
5.
Justify your answer
algebraically.
YOU TRY!
Example 2
Use the graph to
decide whether the
point lies on the graph
of x-2y= 5.
5. Justify
your answer
algebraically.
x - 2y = 5
3 – 2(-4) = 5
3+8=5
11 ≠ 5
No, (3, -4) is not on the line
(5, 0)
x - 2y = 5
a) (3, –4) NO
b) (5, 0)
YES
a) (3, -4)
b) (5, 0)
5 – 2(0) = 5
5-0=5
5=5
Yes, (5, 0) is on the line
Example 3
Decide whether the
ordered pair is a
solution to the
equation y = –2
a) (–2, 2)
b) (–2, –2)
Example 4
y = –2 means that
the y value is –2
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)
(x, y)
Only (b) has the y
value being –2
NO, 2 ≠ -2
Hence, (–2, –2) is the
solution to y = –2
yes, -2 = -2
(b) 2(1) + 4(2) = 8
10≠8 no
Example 1
The Slope Of A Line
Find the slope of the line passing through (-2,-4) and (3,-1).
The slope of the nonvertical line passing through the
points (x1,y1) and (x2,y2) is:
m=
y2 – y1
x2 – x1
=
Solution: Let (x1,y1) = (-2,-4) and (x2,y2) = (3,-1).
y2 – y1
x
y
5
m= x –x
2
1
rise
run
(-1) – (-4)
m = (3) – (-2)
-1 + 4
m=
3+ 2
(x2,y2)
(y2 – y1)
(x1,y1)
rise
m=
(x2 – x1)
-2
-4
4
3
-1
3
2
1
–5 –4
3
5
–3 –2
+3
–1 +5
–1
1
2
3
4
5
4
5
–2
–3
run
–4
–5
Example 2:
Example 3: You try!!
Find the slope of the line passing through (2,-1) and (-3,5).
Find the slope of the line passing through (-4,3) and (-4,5).
Solution: Let (x1,y1) = (2,-1) and (x2,y2) = (-3,5)
y2 – y1
x
y
5
m= x –x
2
1
Solution: Let (x1,y1) = (-4,3) and (x2,y2) = (-4,5)
y2 – y1
x
y
5
m= x –x
2
1
(5) – (-1)
m = (-3) –(2)
5+ 1
m=
-3 - 2
m=
6
-5
2
-1
4
-3
5
3
(5) – (3)
m = (-4) –(-4)
5- 3
m=
-4 + 4
2
-6
1
–5 –4
–3 –2
–1
–1
–2
1
+5
2
3
4
5
m=
2
0
–3
m= - 6
5
–4
–5
-4
3
4
-4
5
3
2
1
–5 –4
–3 –2
–1
–1
–2
–3
m =Undefined
1
2
3
The slope of a
vertical line is??
–4
–5
UNDEFINED!
Example 4
Your homework
Find the value of y .
Given: (2, y), (4, 5), m = 2
y2 – y1
m= x –x
2
1
(5) – (y)
(4) – (2)
5– y
2=
2
4 = 5-y
2=
y=1
x
y
2
y
4
5
Use DCMAM!
y2 – y1
m= x –x
2
1
m=
5– 1
4– 2
m=
4
2
m=2
1. Verifying a Point on a Line wkst
*Show your work!
2. pp. 230-231
*Read the directions carefully! For some
problems, you need to plot the points, find the
slope, and explain why.