Final answer:
The line equation 3x + 5y = 2 has a slope of -3/5 and a y-intercept of 2/5. The correct graph of this line will show a downward trend as the x-value increases due to the negative slope. Options describing other slopes or y-intercepts are incorrect.
Step-by-step explanation:
The equation 3x + 5y = 2 represents a straight line. To find the slope of this line, we need to rewrite the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Subtracting 3x from both sides of the equation yields 5y = -3x + 2. Dividing through by 5 gives y = -½x + ⅔. This reveals that the slope of the line is -3/5 and the y-intercept is 2/5. Therefore, the correct graph of this equation will show a line that decreases by 3 units vertically for every 5 units it moves horizontally, and it crosses the y-axis at 2/5.
The information provided in the options a, c, and d are incorrect for this line as they describe lines with different slopes and/or y-intercepts. So, the line has a negative slope and, contrary to what is stated in option a, it will not rise as the x-value increases. It will actually descend, reflecting the negative slope.