Consider a straight line expressed in point–slope form
MATHEMATICS · Multi-part · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane
Problem
Consider a straight line expressed in point–slope form y−y1=m(x−x1). Answer the following questions.
(i) Write the general form of a linear equation in (a) point–slope form and (b) slope–intercept form, clearly identifying the meaning of each symbol.
(ii) Starting from y−y1=m(x−x1), derive an explicit expression for the y-intercept c in terms of m,x1 and y1.
(iii) Explain, without using a numerical example, why the numerical value of the slope remains unchanged when the equation is rewritten from point–slope form to slope–intercept form.