To find the equation of a line in point-slope form that passes through the points [tex]\((-1, -7)\)[/tex] and [tex]\( (1, 3) \)[/tex], we can follow these steps:
1. Identify the coordinates of the points:
These are given as:
- Point 1: [tex]\((x_1, y_1) = (-1, -7)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (1, 3)\)[/tex]
2. Calculate the slope (m) of the line:
The slope formula is:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the coordinates of the points:
[tex]\[
m = \frac{3 - (-7)}{1 - (-1)} = \frac{3 + 7}{1 + 1} = \frac{10}{2} = 5
\][/tex]
3. Write the point-slope form equation:
The point-slope form of the equation of a line is given by:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Using the slope [tex]\( m = 5 \)[/tex] and the point [tex]\((x_1, y_1) = (-1, -7)\)[/tex]:
[tex]\[
y - (-7) = 5(x - (-1))
\][/tex]
4. Simplify the equation:
We get:
[tex]\[
y + 7 = 5(x + 1)
\][/tex]
Therefore, the equation of the line in point-slope form that passes through the points [tex]\((-1, -7)\)[/tex] and [tex]\( (1, 3) \)[/tex] is:
[tex]\[
y + 7 = 5(x + 1)
\][/tex]
The slope of this line is [tex]\(5\)[/tex].
