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], you can use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given the points [tex]\((45, 26)\)[/tex] and [tex]\((-14, -33)\)[/tex]:
1. Identify the coordinates:
[tex]\[ (x_1, y_1) = (45, 26) \][/tex]
[tex]\[ (x_2, y_2) = (-14, -33) \][/tex]
2. Calculate the difference in the y-coordinates (rise):
[tex]\[ y_2 - y_1 = -33 - 26 = -59 \][/tex]
3. Calculate the difference in the x-coordinates (run):
[tex]\[ x_2 - x_1 = -14 - 45 = -59 \][/tex]
4. Plug these differences into the slope formula:
[tex]\[ \text{slope} = \frac{-59}{-59} \][/tex]
5. Simplify the fraction:
[tex]\[ \frac{-59}{-59} = 1 \][/tex]
So, the slope of the line that passes through the points [tex]\((45, 26)\)[/tex] and [tex]\((-14, -33)\)[/tex] is:
[tex]\[ \text{slope} = 1 \][/tex]
Therefore, the slope can be written as the integer 1.
