To find the slope of a line that passes through two points, [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Given the two points [tex]\((1, -3)\)[/tex] and [tex]\((7, 18)\)[/tex], we can identify:
[tex]\[
x_1 = 1, \quad y_1 = -3, \quad x_2 = 7, \quad y_2 = 18
\][/tex]
We substitute these values into the slope formula:
[tex]\[
m = \frac{18 - (-3)}{7 - 1}
\][/tex]
Next, simplify the numerator and the denominator:
[tex]\[
m = \frac{18 + 3}{7 - 1}
\][/tex]
[tex]\[
m = \frac{21}{6}
\][/tex]
Finally, we simplify the fraction [tex]\(\frac{21}{6}\)[/tex]:
[tex]\[
m = 3.5
\][/tex]
So, the slope of the line that passes through the points [tex]\((1, -3)\)[/tex] and [tex]\((7, 18)\)[/tex] is:
[tex]\[
\boxed{3.5}
\][/tex]
