Final answer:
The slope-intercept form of the equation of a line with an x-intercept of 3 and a y-intercept of -6 is y = 2x - 6.
Step-by-step explanation:
The question at hand involves determining the slope-intercept form of the equation of a line which has an x-intercept of 3 and a y-intercept of -6. To find the slope (m) of the line, we can use the two intercepts provided. The slope is the ratio of the change in y to the change in x (rise over run).
We know that the line crosses the x-axis at (3,0) and the y-axis at (0,-6). The slope can be calculated by the formula m = (y2 - y1) / (x2 - x1). So, m = (0 - (-6)) / (3 - 0) = 6 / 3 = 2.
Now that we have the slope, we can use the y-intercept to write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The equation of the line is therefore y = 2x - 6.