Show the equation of a Line
The diagram shows part of the curve y = 2 − 18 2x + 3 , which crosses the x-axis at A and the y-axis at B. The normal to the curve at A crosses the y-axis at C. Show that the equation of the line AC is 9x + 4y = 27. Find the length of BC. Answer ⤵ Crosses the x-axis means x-intercept when y = 0 y = 2 − 18 2x + 3 ⇒ when y = 0 0 = 2 − 18 2x + 3 0 = 4x + 6 − 18 2x + 3 0 = 4x − 12 12 = 4x 3 = x ⇔ A(3, 0) Crosses the y-axis means y-intercept when x = 0 y = 2 − 18 2x + 3 ⇒ when x = 0 y = 2 − 18 2·0 + 3 y = 2 − 6 y = − 4 ⇔ B(0, −4) The normal to the curve is Perpendicular (⊥) to it, we need the derivative to find its gradient. m 1 = y' = 0 − 0(2x + 3) ...