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

50- 250 is correct i did that one too

step-by-step explanation: