line qr goes through points q(0, 1) and r(2, 7). which equation represents line qr?\n○ $y - 1 = 6x$\n○ $y…
line qr goes through points q(0, 1) and r(2, 7). which equation represents line qr?\n○ $y - 1 = 6x$\n○ $y - 1 = 3x$\n○ $y - 7 = 2x - 6$\n○ $y - 7 = x - 2$
Answer
Explanation:
Step1: Calculate the slope (m)
The slope formula between two points ((x_1, y_1)) and ((x_2, y_2)) is (m=\frac{y_2 - y_1}{x_2 - x_1}). For points (Q(0,1)) and (R(2,7)), (x_1 = 0), (y_1 = 1), (x_2 = 2), (y_2 = 7). So (m=\frac{7 - 1}{2 - 0}=\frac{6}{2}=3).
Step2: Use point - slope form
The point - slope form of a line is (y - y_1=m(x - x_1)). Using point (Q(0,1)) ((x_1 = 0), (y_1 = 1)) and (m = 3), we get (y - 1=3(x - 0)), which simplifies to (y - 1 = 3x). We can also check with point (R(2,7)). Using point - slope form with (R(2,7)) ((x_1 = 2), (y_1 = 7)) and (m = 3), we have (y - 7=3(x - 2)=3x-6), which is equivalent to (y - 7 = 3x-6), and if we rearrange (y - 1 = 3x) (from point (Q)) and check with (x = 2), (y=3\times2 + 1=7), which matches point (R). Let's check the other options:
- For (y - 1=6x), when (x = 2), (y=12 + 1 = 13\neq7), so it's wrong.
- For (y - 7=2x - 6), the slope is 2, but we calculated slope as 3, so it's wrong.
- For (y - 7=x - 2), the slope is 1, which is not equal to 3, so it's wrong.