Final answer:
The equation of the line that is parallel to y=3x+4 and passes through the point (1, -9) is y=3x-12.
Step-by-step explanation:
The student has asked for the written equation of a line that is parallel to another line with the equation y = 3x + 4 and that passes through the point (1, -9).
To find the equation of a line parallel to the given line, we need to use the same slope, which is the m term. Since the given line's equation y = 3x + 4 has a slope of 3, the parallel line will also have a slope of 3.
To write the equation of our new line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through.
Plugging in our slope of 3 and our point (1, -9), we get y - (-9) = 3(x - 1). Simplifying, we find y + 9 = 3x - 3. Subtracting 9 from both sides to put the equation into slope-intercept form (y = mx + b), we get our final answer: y = 3x - 12.