Mathematics
Mathematics
Problem
The linear equation represents a straight line in the Cartesian plane. Answer the questions that follow. a. (i) Write the slope and the -intercept of the line. b. (ii) Determine two additional points with integer coordinates that lie on the line and are convenient for plotting on ordinary graph paper. c. (iii) Sketch the line on a pair of coordinate axes, clearly labelling all intercepts, and hence find the -intercept algebraically. d. (iv) Verify whether the point lies on the line, showing all working.Intuitive explanation
This problem is about understanding the slope-intercept form of a linear equation, where tells you how steeply the line climbs and tells you where it crosses the -axis. The key insight is that these two pieces of information—the rate of change and a single point—completely determine the line's position and direction. You can use them to sketch the graph, find other points, or solve related problems about intersections and relationships with other lines.
Intuitive explanation
This problem is about understanding the slope-intercept form of a linear equation, where tells you how steeply the line climbs and tells you where it crosses the -axis. The key insight is that these two pieces of information—the rate of change and a single point—completely determine the line's position and direction. You can use them to sketch the graph, find other points, or solve related problems about intersections and relationships with other lines.