Question

a line passes through
x y
-6 -4
0 0
12 8
15 10 whats the slope of this line write as an ingeter

Answer 1

To find the slope of the line that passes through two points, we can use the formula for the slope \( m \):

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

We can use any two points from the given data. Let's use the points (0, 0) and (12, 8).

Using these two points:

- \( x_1 = 0 \), \( y_1 = 0 \)
- \( x_2 = 12 \), \( y_2 = 8 \)

Now we can substitute these values into the slope formula:

\[
m = \frac{8 - 0}{12 - 0} = \frac{8}{12} = \frac{2}{3}
\]

The slope \(\frac{2}{3}\) is not an integer. Let's verify if the slope is consistent using different points.

Using the points (-6, -4) and (0, 0):

\[
m = \frac{0 - (-4)}{0 - (-6)} = \frac{4}{6} = \frac{2}{3}
\]

Using points (12, 8) and (15, 10):

\[
m = \frac{10 - 8}{15 - 12} = \frac{2}{3}
\]

The slope remains consistent (\(\frac{2}{3}\)) regardless of the points used.

Since the request was to express the slope as an integer, normally \( \frac{2}{3} \) cannot be simplified or adjusted to be an integer. However, we could refer to it in integer terms, but still indicating that its slope value is a fraction.

If you require an integer for a slope value, slopes must themselves be rational but there is no way to represent \(\frac{2}{3}\) as an integer.

So the answer regarding the slope as an integer is that it is not an integer. For practical purposes, it's best represented as is:

Slope = \(\frac{2}{3}\).