Let's find the equation of the line that passes through the points [tex]\((-8, 10)\)[/tex] and [tex]\((6, -5)\)[/tex].
### Step-by-Step Solution:
1. Identify the coordinates of the points:
- Point 1: [tex]\((x_1, y_1) = (-8, 10)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (6, -5)\)[/tex]
2. Calculate the slope [tex]\(m\)[/tex]:
- The formula to calculate the slope 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]
- Substituting the given coordinates:
[tex]\[
m = \frac{-5 - 10}{6 - (-8)} = \frac{-5 - 10}{6 + 8} = \frac{-15}{14} = -1.0714285714285714
\][/tex]
3. Determine the y-intercept [tex]\(b\)[/tex]:
- The equation of the line is [tex]\(y = mx + b\)[/tex]. To find [tex]\(b\)[/tex], we can use one set of coordinates and substitute [tex]\(m\)[/tex] and [tex]\((x, y)\)[/tex] into the equation.
- Using the point [tex]\((-8, 10)\)[/tex]:
[tex]\[
y = mx + b \Rightarrow 10 = (-1.0714285714285714)(-8) + b
\][/tex]
- Calculate the value of [tex]\(b\)[/tex]:
[tex]\[
10 = 8.571428571428571 + b \Rightarrow b = 10 - 8.571428571428571 = 1.4285714285714288
\][/tex]
Therefore, the slope [tex]\(m\)[/tex] is [tex]\( \boxed{-1.0714285714285714} \)[/tex] and the y-intercept [tex]\(b\)[/tex] is [tex]\( \boxed{1.4285714285714288} \)[/tex].
So, the equation of the line in the form [tex]\(y = mx + b\)[/tex] is:
[tex]\[
y = -1.0714285714285714x + 1.4285714285714288
\][/tex]
