Answer :
To find the slope of the line that passes through the points shown in the table, we need to use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
We can select any two points from the table to calculate the slope. Let's use the points [tex]\((-14, 8)\)[/tex] and [tex]\( (14, 0) \)[/tex].
Using these points, we identify:
- [tex]\( (x_1, y_1) = (-14, 8) \)[/tex]
- [tex]\( (x_2, y_2) = (14, 0) \)[/tex]
Now, substitute these values into the slope formula:
[tex]\[ m = \frac{0 - 8}{14 - (-14)} \][/tex]
Next, let's simplify the expression:
[tex]\[ m = \frac{0 - 8}{14 + 14} \][/tex]
[tex]\[ m = \frac{-8}{28} \][/tex]
[tex]\[ m = -0.2857142857142857 \][/tex]
Thus, the slope of the line that passes through the points in the table is:
[tex]\[ \boxed{-0.2857142857142857} \][/tex]
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
We can select any two points from the table to calculate the slope. Let's use the points [tex]\((-14, 8)\)[/tex] and [tex]\( (14, 0) \)[/tex].
Using these points, we identify:
- [tex]\( (x_1, y_1) = (-14, 8) \)[/tex]
- [tex]\( (x_2, y_2) = (14, 0) \)[/tex]
Now, substitute these values into the slope formula:
[tex]\[ m = \frac{0 - 8}{14 - (-14)} \][/tex]
Next, let's simplify the expression:
[tex]\[ m = \frac{0 - 8}{14 + 14} \][/tex]
[tex]\[ m = \frac{-8}{28} \][/tex]
[tex]\[ m = -0.2857142857142857 \][/tex]
Thus, the slope of the line that passes through the points in the table is:
[tex]\[ \boxed{-0.2857142857142857} \][/tex]
