Question 33

The equation of the line in the xy-plane that passes through the points (1, 0) and (0, 5) is y = -5x + 5.

To find the equation of the line that passes through the points (1, 0) and (0, 5), we can use the slope-intercept form of a line. The slope is calculated as (y2 - y1) / (x2 - x1) = (5 - 0) / (0 - 1) = -5, leading to the equation y = -5x + 5.

A) y = -5x + 1

This option is incorrect because, although it has the correct slope of -5, the y-intercept is not 1, which does not match the point (0, 5). Hence, it does not pass through the correct point on the y-axis.

B) y = -5x + 5

This option is correct as it accurately describes a line with a slope of -5 and a y-intercept of 5. It passes through both given points: when x = 1, y equals 0, and when x = 0, y equals 5.

C) y = 5x - 5

This option is incorrect because it has a positive slope of 5 and a negative y-intercept. It does not align with the calculated slope and y-intercept derived from the given points, failing to pass through either point.

D) y = 5x + 5

This option is also incorrect due to the positive slope of 5 and a y-intercept of 5. Similar to Option C, it does not correspond with the slope or intercept needed to pass through the points (1, 0) and (0, 5).

Conclusion

The correct answer is definitively B) y = -5x + 5, as it accurately represents the line passing through the points (1, 0) and (0, 5 with the correct slope and intercept. All other options fail to meet the criteria established by the given points, either through incorrect slope or intercept values.