To find the slope of the line that passes through the points [tex]\((-5, 6)\)[/tex] and [tex]\( (2, 1)\)[/tex], we can use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
where:
- [tex]\( (x_1, y_1) = (-5, 6) \)[/tex]
- [tex]\( (x_2, y_2) = (2, 1) \)[/tex]
Now, let's substitute the coordinates into the formula:
[tex]\[ m = \frac{1 - 6}{2 - (-5)} \][/tex]
Simplify inside the numerator and denominator:
[tex]\[ m = \frac{1 - 6}{2 + 5} \][/tex]
[tex]\[ m = \frac{-5}{7} \][/tex]
So, the slope [tex]\( m \)[/tex] of the line passing through the points [tex]\((-5, 6)\)[/tex] and [tex]\( (2, 1)\)[/tex] is:
[tex]\[ m = -\frac{5}{7} \][/tex]
### Interpretation of the Slope:
The slope [tex]\( -\frac{5}{7} \)[/tex] represents the rate of change of [tex]\( y \)[/tex] with respect to [tex]\( x \)[/tex]. This means that for every increase of 1 unit in [tex]\( x \)[/tex], the value of [tex]\( y \)[/tex] decreases by [tex]\( \frac{5}{7} \)[/tex] of a unit.
In other words, the line is descending as we move from left to right, which indicates a negative slope. This descent means that as [tex]\( x \)[/tex] increases, [tex]\( y \)[/tex] decreases.
