To find the slope of the line that passes through the given points, we can use the slope formula, which is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
First, let's verify the slope between successive pairs of points to ensure they all lie on a straight line.
### Calculate the slope between the first two points [tex]\((-7, 21)\)[/tex] and [tex]\((-6, 17)\)[/tex]:
[tex]\[ m_1 = \frac{17 - 21}{-6 - (-7)} = \frac{17 - 21}{-6 + 7} = \frac{-4}{1} = -4 \][/tex]
### Calculate the slope between the next pair of points [tex]\((-6, 17)\)[/tex] and [tex]\((-5, 13)\)[/tex]:
[tex]\[ m_2 = \frac{13 - 17}{-5 - (-6)} = \frac{13 - 17}{-5 + 6} = \frac{-4}{1} = -4 \][/tex]
### Calculate the slope between the last two points [tex]\((-5, 13)\)[/tex] and [tex]\((-4, 9)\)[/tex]:
[tex]\[ m_3 = \frac{9 - 13}{-4 - (-5)} = \frac{9 - 13}{-4 + 5} = \frac{-4}{1} = -4 \][/tex]
Since all the calculated slopes ([tex]\(m_1\)[/tex], [tex]\(m_2\)[/tex], and [tex]\(m_3\)[/tex]) are [tex]\(-4\)[/tex], we can conclude that the slope of the line passing through these points remains consistent.
### Final slope of the line:
[tex]\[ \boxed{-4} \][/tex]
This indicates that the line has a consistent slope of [tex]\(-4\)[/tex] between each of the pairs of points provided, confirming that they all lie on a straight line with this constant slope.
