Question

line qr goes through points q(0, 1) and r(2, 7). which equation represents line qr?
○ $y - 1 = 6x$
○ $y - 1 = 3x$
○ $y - 7 = 2x - 6$
○ $y - 7 = x - 2$

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 \(R(2,7)\), we have \(x_1 = 0,y_1 = 1,x_2=2,y_2 = 7\). So \(m=\frac{7 - 1}{2 - 0}=\frac{6}{2}=3\).

Step2: Use point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\). We can use point \(Q(0,1)\) (\(x_1 = 0,y_1 = 1\)) and \(m = 3\). Substituting these values into the point - slope form, 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 \(x_1 = 2,y_1 = 7\) and \(m = 3\), we have \(y - 7=3(x - 2)=3x-6\). Let's check the third option: \(y - 7=2x - 6\) has a slope of 2, which is incorrect. The fourth option \(y - 7=x - 2\) has a slope of 1, incorrect. The first option \(y - 1=6x\) has a slope of 6, incorrect. The second option \(y - 1 = 3x\) has a slope of 3 and when \(x = 0\), \(y=1\) (matches point \(Q\)), when \(x = 2\), \(y=1 + 3\times2=7\) (matches point \(R\)).

Answer:

\(y - 1=3x\) (the second option: \(y - 1 = 3x\))