Final answer:
The gradient of the straight line given by the equation 2y = 3x + 4 is (3/2), and the line crosses the y-axis at the point (0, 2).
Step-by-step explanation:
To find the gradient of the straight line with the equation 2y = 3x + 4, we first need to express it in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. By dividing the entire equation by 2, we obtain y = (3/2)x + 2.
Therefore, the gradient of the line (the slope) is (3/2), which indicates that there is a rise of 3 units on the vertical axis for every run of 2 units on the horizontal axis. The slope is constant along the entire length of a straight line.
To determine the coordinate of the point where the line crosses the y-axis, look at the y-intercept, b, in the equation. Since it's already in the slope-intercept form, the y-intercept is the constant term, +2. This implies that the line crosses the y-axis at the point (0, 2).