To find the equation of the line that intersects the points [tex]\((5, 4)\)[/tex] and [tex]\((7, 8)\)[/tex] in point-slope form, we will follow these steps:
1. Identify the given points:
- Point 1: [tex]\((x_1, y_1) = (5, 4)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (7, 8)\)[/tex]
2. Calculate the slope (m) of the line:
The slope [tex]\( m \)[/tex] is given by the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the given points:
[tex]\[
m = \frac{8 - 4}{7 - 5} = \frac{4}{2} = 2.0
\][/tex]
3. Write the equation in point-slope form:
The point-slope form of the equation of a line is:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Using the slope calculated and the point [tex]\((5, 4)\)[/tex]:
[tex]\[
y - 4 = 2.0(x - 5)
\][/tex]
Thus, the equation of the line in point-slope form is:
[tex]\[
y - 4 = 2.0(x - 5)
\][/tex]
