Question

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

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 \(R(2,7)\). Substitute \(x = 2\) and \(y = 7\) into \(y - 1=3x\): \(7 - 1=3\times2\), \(6 = 6\), which is true. Let's check other options:

• For \(y - 7=2x - 6\), substitute \(x = 0,y = 1\): \(1 - 7=2\times0 - 6\), \(- 6=-6\). But the slope we calculated is 3, not 2. So this is wrong.
• For \(y - 1=6x\), the slope is 6, which does not match our calculated slope of 3.
• For \(y - 7=x - 2\), the slope is 1, which does not match our calculated slope of 3.

Answer:

\(y - 1 = 3x\) (the first option)