Find the x-intercept and y-intercept of the line 4x - 3y = 12.

1. To find the x-intercept, let y equal 0: 4x minus 3 times 0 equals 12, so 4x equals 12 and x equals 3, giving (3, 0). 2. To find the y-intercept, let x equal 0: 4 times 0 minus 3y equals 12, so negative 3y equals 12 and y equals negative 4, giving (0, -4). 3. The intercepts are the points (3, 0) and (0, -4). 4. Flipping the sign on the x-intercept to get (-3, 0) does not match the positive value that solving 4x equals 12 actually produces. 5. Swapping which coordinate is zero, as in (0, 3) and (-4, 0), places the intercepts on the wrong axes entirely. 6. Dropping the negative sign on the y-intercept to report (4, 0) and (0, -3) mixes up both the value and which axis it belongs to. _Source: OpenStax Prealgebra (CC BY 4.0), Ch 11 "Graphs", section 11.3 Graphing with Intercepts_