Final answer:
A solution on the graph of the equation -3x + 6y + 5 = -7 can be found by rearranging the equation to the slope-intercept form, which is y = 0.5x - 2. The point (2, -1) is a solution as it satisfies the original equation.
Step-by-step explanation:
To find a coordinate point that represents a solution on the graph of the equation -3x + 6y + 5 = -7, we need to first rearrange the equation into slope-intercept form (y = mx + b), where 'm' represents slope and 'b' represents the y-intercept. By adding 3x to both sides and then subtracting 5 from both sides, the equation becomes 6y = 3x - 12. Dividing through by 6 yields y = 0.5x - 2.
Now, we can use the information given in the reference, which shows a graph with a slope of 3 and a y-intercept of 9 (y = 9 + 3x). However, this information seems to refer to a different equation than the one we are working with, so we will ignore it here.
Back to our slope-intercept equation, we can choose any value for 'x' to find a corresponding 'y' that lies on the line of our equation. Let's choose x = 2. Substituting x = 2 into y = 0.5x - 2 gives us y = 0.5(2) - 2, which simplifies to y = 1 - 2, thus y = -1. Therefore, the coordinate point (2, -1) is a solution on the graph of the equation -3x + 6y + 5 = -7, as plugging these values into the equation confirms the left-hand side equals the right-hand side.