What is an equation of the line that passes through the point (6,7) and is parallel to the line
2x−3y=9?

The equation of line parallel to given line passing through (6,7) is:

Step-by-step explanation:

Given equation of line is:

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

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

Dividing whole equation by 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:

Putting the point (6,7) in equation

Putting the value of b

Hence,

The equation of line parallel to given line passing through (6,7) is:

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c

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step-by-step explanation: