The slope-intercept form of a line is y equals m x plus b, where m represents the slope and b represents the y-intercept. Given a slope of one-half and a y-intercept of zero, the equation becomes y equals one-half x plus zero, which simplifies to y equals one-half x.
The y-intercept is the point where the line crosses the y-axis. Since our y-intercept is zero, the line passes through the origin, which is the point (0, 0). This is where our line will begin.
The slope of one-half means that for every two units we move to the right (the run), we move one unit up (the rise). This creates a right triangle that visually represents the slope of our line.
Starting from the origin (0, 0), we can find additional points by repeatedly applying the slope. Moving right 2 and up 1 from (0, 0) gives us (2, 1). Doing it again gives us (4, 2). Moving in the opposite direction (left 2 and down 1) from (0, 0) gives us (-2, -1).
Now we connect all our plotted points to form the complete line. We add arrows at both ends to show that the line extends infinitely in both directions. The equation y equals one-half x is labeled on the line.
To verify our graph is correct, we can create a table of values. We choose several x-values and calculate the corresponding y-values using our equation y equals one-half x. All the resulting points lie perfectly on our graphed line, confirming its accuracy.
To summarize, our line has the equation y equals one-half x. The slope is one-half, which is positive, meaning the line rises from left to right. The y-intercept is zero, so the line passes through the origin. This represents a direct proportional relationship between x and y.