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

Answer 1

To find the equation of line QR that goes through points Q(0, 1) and R(2, 7), we first need to determine the slope of the line.

The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the coordinates of points Q and R:

- \(Q(0, 1)\) means \(x_1 = 0\) and \(y_1 = 1\)
- \(R(2, 7)\) means \(x_2 = 2\) and \(y_2 = 7\)

Now plug in the values:

\[
m = \frac{7 - 1}{2 - 0} = \frac{6}{2} = 3
\]

Now that we have the slope, we can use the point-slope form of the equation of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

Using point Q(0, 1) and slope \(m = 3\):

\[
y - 1 = 3(x - 0)
\]

This simplifies to:

\[
y - 1 = 3x
\]

Rearranging gives us:

\[
y = 3x + 1
\]

Now let's compare this result with the given answer choices.

The rearranged equation corresponds to:

1. **y – 1 = 3x** (correct - matches our equation)
2. y – 1 = 6x (not correct)
3. y – 7 = 2x – 6 (not correct)
4. y – 7 = x – 2 (not correct)

Thus, the correct equation representing line QR is:

**y – 1 = 3x.**