To determine the slope of the line that contains the given points, let's follow the step-by-step solution:
1. Identify the points:
- Our given points are [tex]\((-7, -7)\)[/tex], [tex]\((-4, 14)\)[/tex], [tex]\((-1, 35)\)[/tex], and [tex]\( (2, 56) \)[/tex].
2. Select two points to calculate the slope:
- We can use any two points to find the slope, but for simplicity, we'll use the first two points [tex]\((-7, -7)\)[/tex] and [tex]\((-4, 14)\)[/tex].
3. Calculate the differences between the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates:
- Difference in [tex]\(x\)[/tex] (denoted as [tex]\(\Delta x\)[/tex]):
[tex]\[
\Delta x = -4 - (-7) = -4 + 7 = 3
\][/tex]
- Difference in [tex]\(y\)[/tex] (denoted as [tex]\(\Delta y\)[/tex]):
[tex]\[
\Delta y = 14 - (-7) = 14 + 7 = 21
\][/tex]
4. Calculate the slope:
- The slope ([tex]\(m\)[/tex]) of a line is given by the formula:
[tex]\[
m = \frac{\Delta y}{\Delta x}
\][/tex]
- Substituting the values we calculated:
[tex]\[
m = \frac{21}{3} = 7
\][/tex]
Therefore, the slope of the line that contains the given points is:
[tex]\[
\boxed{7}
\][/tex]
