Final answer:
The equation of the line with a slope of 3 that passes through the point (1, 8) is derived using the point-slope formula, resulting in y = 3x + 5. The correct answer is option a) y = 3x + 5.
Step-by-step explanation:
To find the equation for the line with a slope of 3 that goes through the point (1, 8), we can use the point-slope formula for a linear equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.
Plugging in our point (1, 8) and slope 3, the equation becomes:
y - 8 = 3(x - 1). Expanding this, we get y - 8 = 3x - 3. To find the form y = mx + b, we add 8 to both sides of the equation, resulting in y = 3x + 5.
Therefore, the correct answer is a) y = 3x + 5.