Final answer:
The standard form of the line with an x-intercept of 3 and a y-intercept of 4 is 4x + 3y = 12. This is found by determining the slope from the intercepts and converting the slope-intercept form of the equation to standard form.
Step-by-step explanation:
To find the standard form of a line with an x-intercept of 3 and a y-intercept of 4, we can use the intercepts to write the equation of the line. The standard form of a linear equation is usually expressed as Ax + By = C, where A, B, and C are integers, and A is non-negative.
Since the x-intercept is 3, the point (3, 0) lies on the line, and since the y-intercept is 4, the point (0, 4) lies on the line as well. We can use these two points to find the slope (m) of the line using the slope formula m = (y2 - y1) / (x2 - x1). Substituting the points gives us:
m = (4 - 0) / (0 - 3) = -4/3.
Now, we can use the slope-intercept form y = mx + b and plug in the slope and y-intercept:
y = (-4/3)x + 4.
To convert this equation to standard form, we'll clear the fraction by multiplying each term by 3:
3y = -4x + 12.
Finally, arrange the equation to get:
4x + 3y = 12.
Therefore, the correct standard form of the line is 4x + 3y = 12, which corresponds to option D.