To find the slope of the line that passes through the points [tex]\((-20, 18)\)[/tex] and [tex]\( (30, 14) \)[/tex], we use the formula for the slope [tex]\( m \)[/tex]:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, [tex]\( (x_1, y_1) = (-20, 18) \)[/tex] and [tex]\( (x_2, y_2) = (30, 14) \)[/tex].
1. Calculate the difference in the y-coordinates (numerator):
[tex]\[ y_2 - y_1 = 14 - 18 = -4 \][/tex]
2. Calculate the difference in the x-coordinates (denominator):
[tex]\[ x_2 - x_1 = 30 - (-20) = 30 + 20 = 50 \][/tex]
3. Substitute these values into the slope formula:
[tex]\[ m = \frac{-4}{50} \][/tex]
4. Simplify the fraction:
[tex]\[ \frac{-4}{50} = -\frac{2}{25} \][/tex]
So, the slope of the line passing through the points [tex]\((-20, 18)\)[/tex] and [tex]\( (30, 14) \)[/tex] is:
[tex]\[ -\frac{2}{25} \][/tex]
Thus, the correct answer is:
[tex]\[ -\frac{2}{25} \][/tex]
