Consider the two linear equations y=2x+1 and y=−23x+1. Answer the following:
(i) Explain how the numerical value and sign of the coefficient of x affect the inclination of a straight line with respect to the positive x-axis.
(ii) Without plotting any points, state which of the two lines rises as x increases and which one falls. Give reasons for your answer.
(iii) Sketch both lines on the same Cartesian plane, clearly marking the y-intercepts and one additional convenient point on each line.
(iv) From your sketch, describe which line is steeper and justify the observation in terms of the coefficients of x.