find the equation of the line through (1,5) and parallel to y=2x/3+1

Question

find the equation of the line through the given point and parallel to the given line.

point; (1,5)

line; y= 2x/3 + 1

Answer 1

y = (2/3)x + 1 is the slope-intercept form of the equation of the line. The coefficient of x is 2/3, making this the slope of the line. Any line parallel to this must also have slope 2/3.

 

The point-slope form of the equation of the line in question is

 

y - y₁ = m (x - x₁)

 

Setting x₁ = 1, y₁ = 5, m = 2/3. this yields

 

y - 5 = 2/3 (x - 1)

 

Converting to slope-intercept form:

 

y - 5 = (2/3) x - 2/3

y - 5 + 5 = (2/3) x - 2/3 + 5
y = (2/3) x - 2/3 + 15/3

y = (2/3) x + 13/3