Question

A line passes through the points in this table.
x y
-5 29
0 22
15 1
25 -13
What is the slope of the line?
Write your answer as an integer or simplified fraction.

Answer 1

To find the slope of the line that passes through the given points, we can use the slope formula, which is defined as:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

where \( (x_1, y_1) \) and \( (x_2, y_2) \) are any two points on the line.

Let's use the points \( (0, 22) \) and \( (25, -13) \) for our calculation.

Here, \( x_1 = 0 \), \( y_1 = 22 \), \( x_2 = 25 \), and \( y_2 = -13 \).

Now plug these values into the formula:

\[
m = \frac{-13 - 22}{25 - 0}
\]

Calculating the numerator:

\[
-13 - 22 = -35
\]

Calculating the denominator:

\[
25 - 0 = 25
\]

So now we have:

\[
m = \frac{-35}{25}
\]

This can be simplified. Both -35 and 25 can be divided by 5:

\[
m = \frac{-35 \div 5}{25 \div 5} = \frac{-7}{5}
\]

Therefore, the slope of the line is:

\[
\boxed{-\frac{7}{5}}
\]