When the slope of two lines is equal, then the lines are parallel to each other. The equation of a line passing through the point (6,1) and parallel to the line whose equation [tex]3x=2y+4[/tex] is [tex]2y=3x-16[/tex].
Given,
The equation [tex]3x=2y+4[/tex] of the parallel line.
Passing through the point ( 6, 1 ).
To find: Equation of the line.
Now,
The slope-intercept form of the line is [tex]y=mx+c[/tex].
Where m is the slope of the line.
Comparing the given equation [tex]3x=2y+4[/tex] from standard equation of line.
Thus, the slope of the line is 3/2.
Therefore both the lines are parallel to each other, thus the slope of desired line will also be 3/2.
Substitute the value of slope in slope-intercept form.
[tex]y=(3/2)x+c\\2y=3x+c[/tex]
Since the line is passing through the point ( 6, 1 ).
Therefore, the point satisfies the equation of the line.
[tex]2 \times 1=3 \times 6+c\\c=-16[/tex]
Put the value of c in the above equation.
[tex]2y=3x-16[/tex]
Thus, the equation of the line is [tex]2y=3x-16[/tex]
To know more about the slope-intercept form, please refer to the link:
https://brainly.com/question/20786109
