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What is the slope of the line that passes through the points [tex]$(-20, 18)$[/tex] and [tex]$(30, 14)$[/tex]?

A. [tex]$-\frac{25}{2}$[/tex]
B. [tex]$-\frac{5}{2}$[/tex]
C. [tex]$-\frac{2}{5}$[/tex]
D. [tex]$-\frac{2}{25}$[/tex]


Sagot :

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]