Write the equation of the line that is perpendicular to the line 5y=x−5 through the point (-1,0).A. y= 1/5x+5B. y= 1/5x−5C. y= −5x−5D. y= −5x+5
Accepted Solution
A:
Steps:---> Re arrange equation to get the format: y = mx + c---> Work out the perpendicular gradient from the first equation----> Substitute the x and y coordinates of point (-1, 0) and the perpendicular gradient into y = mx + c and work out c---> Finally, substitute the perpendicular gradient and the value for c into y =mx + c to get the gradient of the perpendicular line:__________________________________________Rearranging equation into the format: y = mx + c:[tex]5y = x - 5[/tex] (Just divide both sides by y)[tex]y = \frac{1}{5}x -1[/tex] ___________________________________________Working out the perpendicular gradient:To work out the perpendicular gradient, we just take the negative reciprocal of the gradient of [tex]y = \frac{1}{5}x -1[/tex] Note: negative reciprocal means we just flip the fraction and put a minus sign.The regular gradient is: [tex]\frac{1}{5}[/tex]So the perpendicular gradient is the negative reciprocal of [tex]\frac{1}{5}[/tex]which is -5 (note: [tex]\frac{-5}{1}[/tex] is just 5-)___________________________________________Now lets substitute in the values for the gradient (m), the y coord (0) and x coord (-1) of the point (-1, 0) into y = mx + c, and solve for c:y = mx + c (substitute in all known values)0 = -5(-1) + c (the -1 times -5 will make + 5)0 = 5 + c (subtract 5 from both sides to cancel out the + 5)-5 = cso c = -5____________________________________________Finally, just substitute in the perpendicular gradient and the value for c into y = mx + c to get the equation of the perpendicular line:y = mx + c (substitute in the perp. gradient and c)y = -5x - 5____________________________________________________Answer:The equation to the line perpendicular to 5y = x - 5 through point (-1, 0) is :C. y = -5x - 5_______________________________________________A quicker way to get equation of the perpendicular line once you know the perp. gradient is to use the equation:y - y1 = m (x - x1)y1 is the y coordinate of (-1, 0)x1 is the x coordinate of (-1, 0)m is the perpendicular gradient.y - y1 = m (x - x1) (Substitute in values)y - 0 = -5 ( x - - 1) (simplify)y = -5 (x + 1) (expand the brackets)y = -5x - 5