Sure, I can help you understand how to form the equation of a line given a point and a slope. Let's solve this step-by-step.
### Problem Statement:
- Given point: [tex]\( (4, 2) \)[/tex]
- Given slope: [tex]\( 3 \)[/tex]
### Goal:
- Form the equation of the line using the point-slope form.
### Steps:
1. Understand the point-slope form:
The point-slope form of the equation of a line is given by:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope.
2. Identify the given values:
- Point [tex]\( (x_1, y_1) = (4, 2) \)[/tex]
- Slope [tex]\( m = 3 \)[/tex]
3. Substitute the given values into the point-slope form:
- Substitute [tex]\( x_1 = 4 \)[/tex], [tex]\( y_1 = 2 \)[/tex], and [tex]\( m = 3 \)[/tex] into the equation:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Substituting the values, we get:
[tex]\[
y - 2 = 3(x - 4)
\][/tex]
4. Write down the final equation:
The equation of the line in point-slope form with the given point and slope is:
[tex]\[
y - 2 = 3(x - 4)
\][/tex]
Thus, the equation of the line that passes through the point [tex]\((4, 2)\)[/tex] with a slope of [tex]\(3\)[/tex] is:
[tex]\[ y - 2 = 3(x - 4) \][/tex]
