Final answer:
The gradient of the line that is perpendicular to the line 2y = 3 + 5x is found to be -0.4, after converting the given equation to slope-intercept form and determining the negative reciprocal of the original slope.
Step-by-step explanation:
To find the gradient of a line that is perpendicular to the given line 2y = 3 + 5x, we first need to put the given equation in slope-intercept form (y = mx + b). By dividing everything by 2, we get y = 2.5x + 1.5, where the gradient (or slope) of this line is 2.5. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the line perpendicular to the given one is -1/2.5, which simplifies to -0.4. Therefore, the gradient of the line that is perpendicular to the line 2y = 3 + 5x is -0.4.