Question

Lena says that the point (2,7) lies on the line y= 1/2 x+6. Is Lena correct and why?

a. Yes. Lena is correct because 2 = 1/2 (7)+6.
b. Yes. Lena is correct because 7 = x 1/2(2)+6.
c. No. Lena is incorrect because 2 ≠ 1/2 (7)+6.
d. No. Lena is incorrect because 7 ≠ 1/2 (2)+6.

Answer 1

Lena is correct. The point (2,7) lies on the line y = 1/2 x + 6, as substituting the x-value 2 into the equation yields a y-value of 7, matching the point's y-coordinate.

Step-by-step explanation:

Lena states that the point (2,7) lies on the line y = 1/2 x + 6. To verify this, we need to plug the x-value of the point into the equation and see if the resulting y-value matches the y-value of the point. Let's substitute x = 2 into the equation:

y = 1/2 * 2 + 6
y = 1 + 6
y = 7

The computed y-value is indeed 7, which matches the y-value given in the point (2,7). Therefore, Lena is correct, and the point (2,7) lies on the given line. The correct answer is option b.