The intercepts are the points where the graph cuts the axis. The x-intercept the point where the graph cuts the x-axis, and the y-intercept the point where the graph cuts the y-axis.
The graph cuts the x-axis when the y value is equal to zero, therefore, our x-intercept is (x, 0). To find the corresponding x-value, we just need to evaluate y = 0 on the equation.
![0=-x+3\Rightarrow x=3](https://img.qammunity.org/2023/formulas/mathematics/college/3iyfc2joqmtkj5jd6wd78vxjdwe6q2i27h.png)
The x-intercept is (3, 0).
The graph cuts the y-axis when the x value is equal to zero, therefore, our y-intercept is (0, y). To find the corresponding y-value, we just need to evaluate x = 0 on the equation.
![y=0+3\Rightarrow y=3](https://img.qammunity.org/2023/formulas/mathematics/college/vfl7p5dgn9p6gfl099tqust9jdtq5k2tyk.png)
The y-intercept is (0, 3).