Find the x-intercept and y-intercept of the line 2x + y = 6.

1. To find the x-intercept, let y equal 0: 2x plus 0 equals 6, so 2x equals 6 and x equals 3, giving (3, 0). 2. To find the y-intercept, let x equal 0: 2 times 0 plus y equals 6, so y equals 6, giving (0, 6). 3. The intercepts are the points (3, 0) and (0, 6). 4. Swapping which coordinate is zero in each pair, as in (0, 3) and (6, 0), reverses the intercepts and puts them on the wrong axes. 5. Listing the intercepts as (6, 0) and (0, 3) keeps the zeros in the right slots but uses the wrong numbers, since neither substitution actually produces those values. 6. Reporting (2, 0) and (0, 1) divides the correct intercepts in half instead of solving the equation directly. _Source: OpenStax Prealgebra (CC BY 4.0), Ch 11 "Graphs", section 11.3 Graphing with Intercepts_