Final answer:
The equation of the line with a slope of 3 that passes through (1,5) is y = 3x + 2, which can be found using the point-slope form. The correct option answer from the choices provided is B) y=3x+2.
Step-by-step explanation:
The student is asking for the equation of a line with a slope of 3 that passes through the points (1,5) and (−3,−7). To find the equation of this line, we use the point-slope form of a line which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point the line passes through.
Let's use point (1,5):
y - 5 = 3(x - 1)
y - 5 = 3x - 3
y = 3x - 3 + 5
y = 3x + 2
Therefore, the correct equation of the line is y = 3x + 2. Checking the given choices, option B) y=3x+2 is the correct option answer.
When we solve the mathematical problem completely, we consider that the slope of the line given by the two points should match the slope mentioned in the question. However, since the slope is already provided, we only used one point to establish the equation of the line.