Final answer:
The slope of the line passing through the points (0,5) and (5,5) is calculated to be 0, meaning the line is horizontal.
Step-by-step explanation:
The question involves finding the slope of a line that passes through two points. To calculate the slope, also known as the rise over run, we use the formula m = (Y2 - Y1) / (X2 - X1). When we apply the formula to the points (0,5) and (5,5), we get m = (5 - 5) / (5 - 0), which simplifies to m = 0 / 5. Therefore, the slope of the line is 0, indicating that the line is horizontal.
To find the slope of a line passing through two points, you can use the slope formula:
Slope
(
�
)
=
�
2
−
�
1
�
2
−
�
1
Slope(m)=
x
2
−x
1
y
2
−y
1
Given two points
(
�
1
,
�
1
)
(x
1
,y
1
) and
(
�
2
,
�
2
)
(x
2
,y
2
), plug in these coordinates into the formula. For example, let's consider points
(
�
1
,
�
1
)
=
(
2
,
3
)
(x
1
,y
1
)=(2,3) and
(
�
2
,
�
2
)
=
(
5
,
8
)
(x
2
,y
2
)=(5,8):
Slope
=
8
−
3
5
−
2
=
5
3
Slope=
5−2
8−3
=
3
5
The resulting fraction,
5
3
3
5
, represents the slope of the line passing through the given pair of points.
It's important to note that the slope is the ratio of the vertical change (difference in y-coordinates) to the horizontal change (difference in x-coordinates) between two points on the line. This formula works for any pair of distinct points on a line.