To determine the equation of the line in point-slope form using the point [tex]\((3, 2)\)[/tex], follow these steps:
1. Find the slope of the line:
The slope [tex]\( m \)[/tex] can be calculated using the given points [tex]\((x_1, y_1) = (3, 2)\)[/tex] and [tex]\((x_2, y_2) = (4, 5)\)[/tex].
The formula for the slope is:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Plugging in the values:
[tex]\[
m = \frac{5 - 2}{4 - 3} = \frac{3}{1} = 3.0
\][/tex]
2. 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]
Here, [tex]\( (x_1, y_1) = (3, 2) \)[/tex] and [tex]\( m = 3.0 \)[/tex], so we substitute these values into the equation:
[tex]\[
y - 2 = 3.0(x - 3)
\][/tex]
Therefore, the equation of the line in point-slope form using the point [tex]\( (3, 2) \)[/tex] is:
[tex]\[
y - 2 = 3.0(x - 3)
\][/tex]
