Question

What is an equation of the line that passes through the point

Answer 1

Answer:

The equation of line parallel to given line passing through (6,7) is: $y = \frac{2}{3}x+3$

Step-by-step explanation:

Given equation of line is:

$2x-3y = 9$

We have to convert the equation in slope-intercept form. The slope-intercept form is given by:

$y= mx+b$

Adding 3y on both sides and subtracting 9 from both sides

$2x-3y+3y-9 = 9+3y-9\\2x-9 = 3y\\3y = 2x-9$

Dividing whole equation by 3

$\frac{3y}{3} = \frac{2x-9}{3}\\y = \frac{2}{3}x - \frac{9}{3}\\y = \frac{2}{3}x-3$

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:

$y = m_1x +b\\y = \frac{2}{3}x+b$

Putting the point (6,7) in equation

$7 = \frac{2}{3}(6) +b\\7 = 2(2) +b\\7 = 4+b\\b = 7-4\\b = 3$

Putting the value of b

$y = \frac{2}{3}x+3$

Hence,

The equation of line parallel to given line passing through (6,7) is: $y = \frac{2}{3}x+3$