Answer:
Equation of line passing through (3,2) and parallel to line [tex]y = \frac{1}{3}x-3[/tex] is:
[tex]y = \frac{1}{3}x+1[/tex]
Step-by-step explanation:
Given equation of line is:
[tex]y = \frac{1}{3}x-3[/tex]
Slope-intercept form of a line is given by:
[tex]y = mx+b[/tex]
Comparing the given equation of line with general form we get
m = 1/3
Let m1 be the slope of line parallel to given line
Then the equation of line will be:
[tex]y = m_1x+b[/tex]
We know, "Slopes of two parallel lines are equal"
Which means
[tex]m_1 = m\\m_1 = \frac{1}{3}[/tex]
Putting the value of slope
[tex]y = \frac{1}{3}x+b[/tex]
Putting the point (3,2) in the equation
[tex]2 = \frac{1}{3}(3)+b\\2 = 1+b\\b = 2-1\\b = 1[/tex]
Final equation of line is:
[tex]y = \frac{1}{3}x+1[/tex]
Hence,
Equation of line passing through (3,2) and parallel to line [tex]y = \frac{1}{3}x-3[/tex] is:
[tex]y = \frac{1}{3}x+1[/tex]
