To determine the point-slope equation of the line passing through the points [tex]\((-1, -10)\)[/tex] and [tex]\( (5, 2) \)[/tex], we can follow these steps:
1. Identify the coordinates of the two points:
- Point 1: [tex]\((x_1, y_1) = (-1, -10)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (5, 2)\)[/tex]
2. Calculate the slope (m):
The formula for the slope [tex]\(m\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Plugging in the values [tex]\( (x_1, y_1) = (-1, -10) \)[/tex] and [tex]\( (x_2, y_2) = (5, 2) \)[/tex]:
[tex]\[
m = \frac{2 - (-10)}{5 - (-1)} = \frac{2 + 10}{5 + 1} = \frac{12}{6} = 2
\][/tex]
3. Use the point-slope form of the equation:
The point-slope form of a linear equation is:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Using the slope [tex]\(m = 2\)[/tex] and the point [tex]\((5, 2)\)[/tex]:
[tex]\[
y - 2 = 2(x - 5)
\][/tex]
Therefore, the point-slope equation of the line through [tex]\((-1, -10)\)[/tex] and [tex]\((5, 2)\)[/tex] is:
[tex]\[
y - 2 = 2(x - 5)
\][/tex]
