Answer:
The equation of line parallel to given line passing through (6,7) is: [tex]y = \frac{2}{3}x+3[/tex]
Step-by-step explanation:
Given equation of line is:
[tex]2x-3y = 9[/tex]
We have to convert the equation in slope-intercept form. The slope-intercept form is given by:
[tex]y= mx+b[/tex]
Adding 3y on both sides and subtracting 9 from both sides
[tex]2x-3y+3y-9 = 9+3y-9\\2x-9 = 3y\\3y = 2x-9[/tex]
Dividing whole equation by 3
[tex]\frac{3y}{3} = \frac{2x-9}{3}\\y = \frac{2}{3}x - \frac{9}{3}\\y = \frac{2}{3}x-3[/tex]
Let m be the slope of given line then
m = 2/3
Let m1 be the slope of line parallel to given line. Slopes of two parallel lines is equal that means:
m = m1 = 2/3
The equation of line will be:
[tex]y = m_1x +b\\y = \frac{2}{3}x+b[/tex]
Putting the point (6,7) in equation
[tex]7 = \frac{2}{3}(6) +b\\7 = 2(2) +b\\7 = 4+b\\b = 7-4\\b = 3[/tex]
Putting the value of b
[tex]y = \frac{2}{3}x+3[/tex]
Hence,
The equation of line parallel to given line passing through (6,7) is: [tex]y = \frac{2}{3}x+3[/tex]
