Which of the following is an equation of the line in the xy-plane that passes through the points (1, 0) and (0, 5)?
y = -5x + 5 is the equation of the line that passes through the points (1, 0) and (0, 5).
To find the equation of a line given two points, we first determine the slope and then use the slope-intercept form of the equation. The slope between the points (1, 0) and (0, 5) is calculated as -5, leading to the equation y = -5x + 5.
This equation has the correct slope of -5 but an incorrect y-intercept. If we substitute x = 0, we find that y = 1, which does not match the point (0, 5). Thus, this line does not pass through the required points.
This equation has the correct slope of -5 and a y-intercept of 5. If we substitute x = 0, we get y = 5, which matches the point (0, 5), and substituting x = 1 leads to y = 0, confirming that it passes through both points (1, 0) and (0, 5).
This equation has a slope of 5, which is the opposite of the required slope of -5. Therefore, it does not describe a line that passes through the given points; instead, it would rise rather than fall between the two points.
Similar to option C, this equation has a slope of 5, which is incorrect for the line that connects the points (1, 0) and (0, 5). The positive slope indicates that the line rises, contradicting the downward trend observed between the two specified points.
The equation of the line through the points (1, 0) and (0, 5) is accurately represented by y = -5x + 5, which maintains the correct slope and intercept. The other choices fail either by having the wrong intercepts or incorrect slopes, highlighting the importance of both parameters in defining a line in the xy-plane.
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