Final answer:
The provided equation does not yield any of the answer options when attempting to find the y-intercept and x-intercept. We suspect there is a typo in the equation or the answer choices. Clarification of the accurate equation is needed to solve for the intercepts.
Step-by-step explanation:
To find the y-intercept and x-intercept of the line -5 + 6y = 9, you can set each variable to zero in turn and solve for the other. For the y-intercept, set x = 0; since there's no x in the equation, we simply solve for y:
- -5 + 6y = 9
- 6y = 14
- y = 14/6
- y = 7/3
However, 7/3 is not an option provided in the answers, which suggests there may be an error in the transcription of the equation or the answer choices. Let's consider that there might be a typo in the y-intercept value. Given the options, it seems that the y-intercept should likely be 2/3 (option A and C) instead of 7/3.
For the x-intercept, set y = 0, which simplifies to -5 = 9, an impossibility. This also indicates there may be a mistake, because under normal circumstances, you would rearrange the equation to isolate x and solve for it just as we would for y. If the equation were written correctly to produce one of the given options for the x-intercept, it seems likely that the x term is simply missing from the provided equation.
Without a correct equation or valid options that match the steps for finding intercepts, we're unable to determine the x-intercept based on the information given. If the equation is incorrect as suggested, it is recommended to clarify the accurate equation before solving for the intercepts.