Final answer:
A linear function with a slope of 3 that passes through the point (6, 12) is given by the equation y = 3x - 6, in slope-intercept form.
Step-by-step explanation:
To construct a linear function that passes through the point (6, 12), we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Referring to FIGURE A1, which provides an example where the slope of the line is 3 and the y-intercept is 9, we can use the same slope for our function since we are only provided with a point and not a specific slope requirement. Thus, with the slope m = 3 and our point (6, 12), we can plug these values into the point-slope form.
The equation becomes y - 12 = 3(x - 6). Simplifying this, we distribute the 3 to obtain y - 12 = 3x - 18. Adding 12 to both sides gives us the slope-intercept form y = 3x - 6.
This equation represents a straight line with a slope of 3 that passes through the point (6, 12) and crosses the y-axis at y-intercept -6. Remember, the slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.