To write the equation of the line in slope-intercept form, we will use the information provided: the slope and a point on the line.
1. Identify the given slope (m):
The slope (m) of the line is given as [tex]\(\frac{1}{5}\)[/tex].
2. Identify the given point (x1, y1):
The point provided on the line is [tex]\((0, 6)\)[/tex].
3. Recall the slope-intercept form equation:
The slope-intercept form of a line is given by:
[tex]\[
y = mx + b
\][/tex]
Here, [tex]\(m\)[/tex] is the slope, and [tex]\(b\)[/tex] is the y-intercept (the value of [tex]\(y\)[/tex] when [tex]\(x = 0\)[/tex]).
4. Using the given point to find the y-intercept [tex]\(b\)[/tex]:
We know that when [tex]\(x = 0\)[/tex], the corresponding [tex]\(y\)[/tex]-value is 6. Therefore, the y-intercept [tex]\(b\)[/tex] is directly given by the y-coordinate of the point [tex]\((0, 6)\)[/tex], which is [tex]\(6\)[/tex].
5. Formulate the equation:
Substitute the slope [tex]\(m = \frac{1}{5}\)[/tex] and the y-intercept [tex]\(b = 6\)[/tex] into the slope-intercept form equation:
[tex]\[
y = \left(\frac{1}{5}\right)x + 6
\][/tex]
Therefore, the equation of the line in slope-intercept form is:
[tex]\[
y = 0.2x + 6
\][/tex]
