What is the equation, in standard form, of the line that passes through the points (-3, -4) and (3, -12)?
4x + 3y = -24
To find the equation of the line that passes through the points (-3, -4) and (3, -12), we first calculate the slope and then use the point-slope form to derive the equation before converting it to standard form.
This equation does not correctly reflect the slope calculated from the two points. When substituting the given points into this equation, neither satisfies it, indicating that it does not represent the line connecting the two points.
Substituting either of the points into this equation shows that it does not hold true for both. Thus, this option fails to represent the line that passes through (-3, -4) and (3, -12), as it does not yield a consistent result.
This equation correctly represents the line that passes through the two specified points. The slope between these points is calculated as -4/3, and when using the point-slope formula and simplifying, we arrive at this standard form, confirming that it is indeed the correct answer.
Similar to the previous incorrect options, substituting the given points into this equation results in inconsistencies. Therefore, it does not accurately represent the line through the specified points, failing to maintain the relationship established by the coordinates.
The correct equation, 4x + 3y = -24, accurately describes the line through the points (-3, -4) and (3, -12). The process of calculating the slope and converting to standard form reveals that this equation satisfies both points, while all other options fail to do so, rendering them incorrect. Understanding the relationships between coordinates and their corresponding linear equations is essential for accurately identifying such expressions.
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