It seems there may have been a typo in your question. Can you please clarify the statement so I can provide you with the most accurate answer?
here is the picture
Given the point P = (a, b) and slope m, the point-slope equation is(y - b) = m*(x - a)y - b = mx - may = mx - ma + bwhich can be re-written asy = mx + (b - ma) which is of the slope-intercept form y = mx + c in which c = b - ma.Given the point P = (a, b) and slope m, the point-slope equation is(y - b) = m*(x - a)y - b = mx - may = mx - ma + bwhich can be re-written asy = mx + (b - ma) which is of the slope-intercept form y = mx + c in which c = b - ma.Given the point P = (a, b) and slope m, the point-slope equation is(y - b) = m*(x - a)y - b = mx - may = mx - ma + bwhich can be re-written asy = mx + (b - ma) which is of the slope-intercept form y = mx + c in which c = b - ma.Given the point P = (a, b) and slope m, the point-slope equation is(y - b) = m*(x - a)y - b = mx - may = mx - ma + bwhich can be re-written asy = mx + (b - ma) which is of the slope-intercept form y = mx + c in which c = b - ma.
The product of the slope of a line with the slope of a line perpendicular to it is -1.Or to put it another way, if a line has an equationy = mx + ca line perpendicular to it will have a gradient m' such thatmm' = -1⇒ m' = -1/mand an equation ofy = -1/m x + bwhich can be rearranged to givemy + x = d(where d = mb).There are symbols missing from the question, which I suspect are a plus (+) and an equals (=). They can be inserted in two different ways, leading to two different solutions:2x + y = 4⇒ y = -2x + 4 ⇒ gradient of perpendicular line is -1/-2 = 1/2⇒ perpendicular line is:y = 1/2 x + b⇒ 2y = x + c2x = y + 4⇒ y = 2x - 4 ⇒ gradient of perpendicular line is -1/2 = -1/2⇒ perpendicular line is:y = -1/2 x + b⇒ 2y + x = cNote: there is no one perpendicular line, the value of the constant c will vary depending upon what point the line must pass through.