31. What is the equation, in standard form, of the line that passes through the points (-3, -4) and (3, -12)?
Answer: C
The equation of the line in standard form is 4x + 3y = -24.
The equation of the line that passes through the points (-3, -4) and (3, -12) can be derived from calculating the slope and then converting to standard form. The correct equation, in standard form, is 4x + 3y = -24.
A) 4x + 3y = 24
This option is incorrect because the constant term does not match the calculated equation. The slope and y-intercept derived from the given points lead to a negative constant, not a positive one.
B) 3x + 4y = -25
This option is incorrect as well. When evaluated using the points provided, it does not satisfy the line equation derived from the slope-intercept form. The coefficients and constant do not align with the calculated values.
C) 4x + 3y = -24
This is the correct answer. The line through the points (-3, -4) and (3, -12) has a slope of -2 and, when put into standard form, results in the equation 4x + 3y = -24. This equation accurately reflects the relationship between x and y for the given points.
D) 3x + 4y = -39
This option is incorrect. The coefficients and the constant do not correspond to the line through the specified points. Substituting the points into this equation does not hold true, indicating it does not represent the correct line.
Conclusion
The correct answer, 4x + 3y = -24, accurately represents the line that passes through the points provided. All other options fail to satisfy the conditions established by the points, either through incorrect coefficients or constant terms, validating Option C as the only valid equation.