Answer:
Explanation:
To find the equation of the line that passes through the points (11/12, 1/2) and (13/12, 0), you can use the point-slope form of a linear equation:
�
−
�
1
=
�
(
�
−
�
1
)
y−y
1
=m(x−x
1
)
Where:
(x₁, y₁) is one of the points on the line, in this case, (11/12, 1/2).
m is the slope of the line.
First, calculate the slope (m) using the given points:
�
=
�
2
−
�
1
�
2
−
�
1
=
0
−
1
/
2
13
/
12
−
11
/
12
=
−
1
/
2
2
/
12
=
−
1
/
2
1
/
6
=
−
3
m=
x
2
−x
1
y
2
−y
1
=
13/12−11/12
0−1/2
=
2/12
−1/2
=
1/6
−1/2
=−3
Now that you have the slope (m), you can use either of the given points to write the equation. Let's use (11/12, 1/2):
�
−
1
/
2
=
−
3
(
�
−
11
/
12
)
y−1/2=−3(x−11/12)
Now, you can simplify and write the equation in a more standard form, such as the slope-intercept form (y = mx + b):
�
−
1
/
2
=
−
3
�
+
3
/
4
y−1/2=−3x+3/4
To isolate y, add 1/2 to both sides:
�
=
−
3
�
+
3
/
4
+
1
/
2
y=−3x+3/4+1/2
Combine the constants:
�
=
−
3
�
+
3
/
4
+
2
/
4
y=−3x+3/4+2/4
�
=
−
3
�
+
5
/
4
y=−3x+5/4
So, the equation of the line that passes through the points (11/12, 1/2) and (13/12, 0) is
�
=
−
3
�
+
5
/
4
y=−3x+5/4.