To determine the slope of the line containing the points [tex]\( M(1,3) \)[/tex] and [tex]\( N(5,0) \)[/tex], we use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
where [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] are the coordinates of points [tex]\( M \)[/tex] and [tex]\( N \)[/tex] respectively.
Let's plug in the coordinates:
- [tex]\( x_1 = 1 \)[/tex]
- [tex]\( y_1 = 3 \)[/tex]
- [tex]\( x_2 = 5 \)[/tex]
- [tex]\( y_2 = 0 \)[/tex]
Substitute these values into the slope formula:
[tex]\[ \text{slope} = \frac{0 - 3}{5 - 1} \][/tex]
Calculate the difference in y-coordinates (numerator):
[tex]\[ 0 - 3 = -3 \][/tex]
Calculate the difference in x-coordinates (denominator):
[tex]\[ 5 - 1 = 4 \][/tex]
Now, we can find the slope:
[tex]\[ \text{slope} = \frac{-3}{4} \][/tex]
Therefore, the slope of the line containing points [tex]\( M \)[/tex] and [tex]\( N \)[/tex] is:
[tex]\[ \boxed{-\frac{3}{4}} \][/tex]
