Final answer:
The equation of the line that crosses the y-axis at (0,3) and passes through (4,5) is y = 1/2x + 3, which is obtained by calculating the slope as 1/2 and knowing that the y-intercept is 3.
Step-by-step explanation:
To find the equation of the line that crosses the y-axis at the point (0,3) and passes through the point (4,5), we need to determine the slope and the y-intercept. The slope (m) of a line can be found using two points that lie on the line using the formula m = (y2 - y1) / (x2 - x1). Here, we will use the points (0,3) and (4,5).
To calculate the slope, we subtract the y-coordinate of the first point from the y-coordinate of the second point and divide it by the subtraction of the x-coordinate of the first point from the x-coordinate of the second point:
m = (5 - 3) / (4 - 0) = 2 / 4 = 1/2
Now, we know the line's slope is 1/2, and it crosses the y-axis at 3 (which is the y-intercept). The general form of a line's equation is y = mx + b, where m is the slope and b is the y-intercept. Plugging in our values:
y = (1/2)x + 3
The correct equation of the line is therefore y = 1/2x + 3, matching option (a)