Let line l be given by the equation ax + by = c.

a. write the equation, in slope intercept form, of the line passing through the point (2, 7) and parallel to line l.

b. write the equation, in slope intercept form, of the line passing through the point (2, 7) and perpendicular to line l.

Part A)

Part B)

Step-by-step explanation:

we have the equation of the line L in standard form

isolate the variable y

The slope of the line L is equal to

Part A) Write the equation, in slope intercept form, of the line passing through the point (2, 7) and parallel to line L

Remember that

If two line are parallel, then their slopes are equal

The equation of the line in slope intercept form is equal to

we have

substitute the values and solve for b

The equation of the line is

Part B) Write the equation, in slope intercept form, of the line passing through the point (2, 7) and perpendicular to line L

Remember that

If two line are perpendicular, then the product of their slopes is equal to -1

The equation of the line in slope intercept form is equal to

we have

Find the value of m2

substitute the values and solve for b

The equation of the line is