To determine the equation of the line QR, we first need to find the slope of the line that passes through points [tex]\( Q(0, 1) \)[/tex] and [tex]\( R(2, 7) \)[/tex].
### Step 1: Calculate the Slope
The formula for the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substituting in our points [tex]\( Q(0, 1) \)[/tex] and [tex]\( R(2, 7) \)[/tex]:
[tex]\[ m = \frac{7 - 1}{2 - 0} = \frac{6}{2} = 3 \][/tex]
So, the slope of the line QR is 3.
### Step 2: Use the Point-Slope Form
Next, we'll use the point-slope form of the equation of a line, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
We can use point [tex]\( Q(0, 1) \)[/tex] as [tex]\( (x_1, y_1) \)[/tex] and our calculated slope [tex]\( m = 3 \)[/tex]:
[tex]\[ y - 1 = 3(x - 0) \][/tex]
Simplifying this equation:
[tex]\[ y - 1 = 3x \][/tex]
### Conclusion
The equation of the line QR in point-slope form is:
[tex]\[ y - 1 = 3x \][/tex]
Comparing this with the provided options, we see that the correct answer is:
[tex]\[ y - 1 = 3x \][/tex]
Therefore, the equation that represents line QR is:
[tex]\[ \boxed{y - 1 = 3x} \][/tex]
