Question

Which equation represents a line that passes through (5, 1) and has a slope of ?

1) ?y – 5 = (x –1)
2) y – 5 = 5(x –1)
3) y – 1 = (x –5)
4) y – 1 = 5

Answer 1

The equation that represents a line passing through (5, 1) and has a slope of -1 is y - 1 = (x - 5).

Step-by-step explanation:

The equation that represents a line passing through (5, 1) and has a slope of -1 is option 3) y - 1 = (x - 5). To determine the equation of a line given a point and slope, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Substituting the values, we have y - 1 = -1(x - 5), which simplifies to y - 1 = -x + 5. Rearranging the equation, we get y - x = 4, which is equivalent to the equation in option 3).