Question

Let line L be given by the equation Ax + By = C.

Answer 1

Answer:

Part A) $y=-\frac{A}{B}x+\frac{7B+2A}{B}$

Part B) $y=\frac{B}{A}x+\frac{7A-2B}{A}$

Step-by-step explanation:

we have the equation of the line L in standard form

$Ax+By=C$

isolate the variable y

$By=-Ax+C$

$y=-(A/B)x+C/B$

The slope of the line L is equal to

$m=-A/B$

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

$y=mx+b$

we have

$m=-A/B$

$point (2,7)$

substitute the values and solve for b

$7=(-A/B)(2)+b$

$b=7+2A/B=(7B+2A)/B$

The equation of the line is

$y=-\frac{A}{B}x+\frac{7B+2A}{B}$

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

$m1*m2=-1$

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

$y=mx+b$

we have

$m1=-A/B$

Find the value of m2

$(-A/B)*m2=-1$

$m2=B/A$

$point (2,7)$

substitute the values and solve for b

$7=(B/A)(2)+b$

$b=7-2B/A=(7A-2B)/A$

The equation of the line is

$y=\frac{B}{A}x+\frac{7A-2B}{A}$