To find the slope of the line passing through the points [tex]\( (3, 5) \)[/tex] and [tex]\( (0, -4) \)[/tex], we can use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, the coordinates of the points are:
[tex]\[
(x_1, y_1) = (3, 5)
\][/tex]
[tex]\[
(x_2, y_2) = (0, -4)
\][/tex]
Substitute the coordinates into the slope formula:
[tex]\[
m = \frac{-4 - 5}{0 - 3}
\][/tex]
Calculate the numerator and the denominator separately:
[tex]\[
y_2 - y_1 = -4 - 5 = -9
\][/tex]
[tex]\[
x_2 - x_1 = 0 - 3 = -3
\][/tex]
Now, substitute these values back into the formula:
[tex]\[
m = \frac{-9}{-3}
\][/tex]
Simplify the fraction:
[tex]\[
m = 3
\][/tex]
Therefore, the slope of the line passing through the points [tex]\( (3, 5) \)[/tex] and [tex]\( (0, -4) \)[/tex] is [tex]\( 3 \)[/tex].
