Parallel and perpendicular line (4,7); y3x+6

Parallel Line: y = 3x - 5

Perpendicular Line: y = -1/3x + 25/3

Step-by-step explanation:

The equation given is a linear equation in slope-intercept form, y = mx + b, where m = slope and b = y-intercept.  With lines that are parallel to each other, they containt the same slope.  So, to form an equation of a line that is parallel to the first equation, the slope = 3.  Using the given point (4, 7), x = 4 and y = 7, we can use our slope-intercept form to solve for 'b':

7 = (3)(4) + b or 7 = 12 + b or b = -5

So, our equation for a parallel line would be: y = 3x - 5.

For perpendicular lines, the slope must be the opposite reciprocal of the slope from the first equation.  So, if m = 3, than the slope of the perpendicular line must be - 1/3.  Using the same point (4, 7) we can use our slope-intercept form to solve for 'b':  

7 = (-1/3)(4) + b or 7 = -4/3 + b or b = 25/3

So, our equation for a perpendicular line would be: y = -1/3x + 25/3

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

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step-by-step explanation:

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