Question

Which of the following is the equation of a line parallel to the line y=-X+ 1, passing through the point (4 1)?

A. y = -x + 4
B. x + y = 5
C. x - y = -5
D. xy = 5

Answer 1

The correct equation for a line parallel to y = -x + 1 and passing through the point (4, 1) is x + y = 5, which is Option B.

Step-by-step explanation:

The equation of the line parallel to y = -x + 1 must have the same slope, which is -1. This is because parallel lines have identical slopes. Let's denote the slope as m. Now taking into account the point through which our new line must pass, which is (4, 1), you can use the point-slope form of a line, which is y - y1 = m(x - x1) to plug in our values. Substituting m = -1, x1 = 4, and y1 = 1, we get y - 1 = -1(x - 4). Simplifying this equation gives us y = -x + 5, which in standard form is x + y = 5.

Now, we'll compare this derived equation to the options given:

• Option A: y = -x + 4 is not correct as the y-intercept is different.
• Option B: x + y = 5 is correct as it matches our derived equation.
• Option C: x - y = -5 does not have the correct slope.
• Option D: xy = 5 is not even a linear equation.

Therefore, the correct answer is Option B: x + y = 5, which is the equation of a line parallel to y = -x + 1 and which goes through the point (4, 1).