What is the slope of the line that contains these points?

[tex]\[
\begin{array}{rrrrr}
x & -1 & 0 & 1 & 2 \\
\hline
y & 10 & 18 & 26 & 34
\end{array}
\][/tex]

Slope: [tex]$\square$[/tex]



Answer :

To find the slope of the line that contains the given points, we will use the formula for the slope [tex]\( m \)[/tex] 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]

Let's select the first pair of points from the table provided: [tex]\((-1, 10)\)[/tex] and [tex]\((0, 18)\)[/tex].

1. Identify the coordinates of the first point:
- [tex]\(x_1 = -1\)[/tex]
- [tex]\(y_1 = 10\)[/tex]

2. Identify the coordinates of the second point:
- [tex]\(x_2 = 0\)[/tex]
- [tex]\(y_2 = 18\)[/tex]

3. Substitute these values into the slope formula:

[tex]\[ m = \frac{18 - 10}{0 - (-1)} \][/tex]

4. Calculate the numerator [tex]\( y_2 - y_1 \)[/tex]:

[tex]\[ 18 - 10 = 8 \][/tex]

5. Calculate the denominator [tex]\( x_2 - x_1 \)[/tex]:

[tex]\[ 0 - (-1) = 0 + 1 = 1 \][/tex]

6. Divide the numerator by the denominator to find the slope:

[tex]\[ m = \frac{8}{1} = 8 \][/tex]

Therefore, the slope of the line that contains the given points is:
[tex]\[ \boxed{8} \][/tex]