Question

Graphed points: ( 2,7 ) and ( -1, 1)

What is the system of equations shown in the graph?

A: { y = -x + 1
{ y = 2x + 7

B: { y = 2x - 3
{ y = 3x - 4

C: {y = 2x +3
{y = 3x + 4

D: { y = 3x + 2
{ y = 4x + 3

Answer 1

To determine the correct system of equations based on the given points (2, 7) and (-1, 1), we need to find the equations of lines that pass through these points.

Let's first find the equation of the line that goes through the two points.

1. **Finding the slope (m)**:

Using the formula for the slope:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \((x_1, y_1) = (2, 7)\) and \((x_2, y_2) = (-1, 1)\):
\[
m = \frac{1 - 7}{-1 - 2} = \frac{-6}{-3} = 2
\]

2. **Using point-slope form**:

Using the point-slope form of the equation \(y - y_1 = m(x - x_1)\) with the point (2, 7):
\[
y - 7 = 2(x - 2)
\]
Expanding this gives:
\[
y - 7 = 2x - 4 \quad \Rightarrow \quad y = 2x + 3
\]

Now, we can also find the second line that should intersect the same points.

3. **Finding the second line**

Using the point (−1, 1):
Referencing \(y - 1 = m(x + 1)\) where we need to find the angle, we can assume that it will have a different slope.
If we use the information we found earlier about the first line, we already know the slope is 2.

So we have:
The first line is \(y = 2x + 3\) and now we also could guess a second line to intersect, starting from the y-intercept as such that it will create a system of two lines.

Upon analyzing the given options:

- **Option A** has \(y = 2x + 7\) which doesn't match our derived line \(y = 2x + 3\).
- **Option B** has \(y = 2x - 3\) which matches with \(2x\) but does not meet through the points.
- **Option C** contains \(y = 3x + 4\) does not fulfill our points either.
- **Option D** is incorrect too.

After checking, none of the answer choices seem to contain both correct lines simultaneously.

Thus, based on what we evaluated at the points:
- The first equation we derived is \(y = 2x + 3\).

Thus it seems the given choices might have been misreferenced as typically it would be values intersecting and about to represented.

Nevertheless, for lines intersecting through the points with respect; double-check with the graphical representation of what was calculated -- for future references.