To find the slope of the line that goes through the points [tex]\((2, -15)\)[/tex] and [tex]\((4, 6)\)[/tex], we use the slope formula, which is:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points. Let's plug in the values from the points [tex]\((2, -15)\)[/tex] and [tex]\((4, 6)\)[/tex]:
1. Identify the coordinates:
- [tex]\(x_1 = 2\)[/tex]
- [tex]\(y_1 = -15\)[/tex]
- [tex]\(x_2 = 4\)[/tex]
- [tex]\(y_2 = 6\)[/tex]
2. Substitute these values into the slope formula:
[tex]\[
m = \frac{6 - (-15)}{4 - 2}
\][/tex]
3. Simplify the expression in the numerator and the denominator:
[tex]\[
m = \frac{6 + 15}{4 - 2}
\][/tex]
[tex]\[
m = \frac{21}{2}
\][/tex]
4. Perform the division to find the slope:
[tex]\[
m = 10.5
\][/tex]
So, the slope of the line that goes through the points [tex]\((2, -15)\)[/tex] and [tex]\((4, 6)\)[/tex] is [tex]\(10.5\)[/tex].
