Final answer:
The equation that defines a line with a slope of -4 and an x-intercept of 3 is 4x + y = 12.
Step-by-step explanation:
The equation that defines a line with a slope of -4 and an x-intercept of 3 is 4x + y = 12. The equation of a line can be written in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -4 and the x-intercept is 3. To find the y-intercept, we can substitute the x-intercept into the equation and solve for y. When x = 3, the equation becomes 4(3) + y = 12, which simplifies to 12 + y = 12. Solving for y gives y = 0. Therefore, we have the equation 4x + y = 12.
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