Final answer:
The equation of the line that crosses the y-axis at (0,1) and passes through (2,7) is found by calculating the slope using the two points and applying it to the y=mx+b form. The slope of 3 and the y-intercept of 1 lead to the equation y=3x+1, which corresponds with answer choice B.
Step-by-step explanation:
To find the equation of a line that passes through a certain point and has a specific y-intercept, we need to determine the slope and apply it to the slope-intercept form of a line equation, which is y = mx + b, where m is the slope and b is the y-intercept.
In this case, the line crosses the y-axis at the point (0,1), which means the y-intercept b is 1. It also passes through the point (2,7). To find the slope m, we use the formula (change in y) / (change in x), which would be (7 - 1) / (2 - 0) = 6 / 2 = 3. Thus, the slope of the line is 3.
Now, we can plug in our values for m and b into the equation y = mx + b, which gives us the equation y = 3x + 1. Comparing this to the answer choices, we can see that the correct answer is B. y=3x+1.