Question

x y x y
-3 8 -3 -2
-2 10 -2 0
-1 12 -1 2
0 14 0 4
1 16 1 6
2 18 2 8
3 20 3 10
4 22 4 12

Both of these tables represent linear graphs:



Does the line through the first set of points intersect with the line through the second set of points?

(1 point)
Responses

You cannot tell without a graph
You cannot tell without a graph

No…these lines are parallel
No…these lines are parallel

Yes…these lines are not parallel nor perpendicular
Yes…these lines are not parallel nor perpendicular

No…these lines are perpendicular
No…these lines are perpendicular

Yes…these lines are parallel
Yes…these lines are parallel

Yes…these lines are perpendicular
Yes…these lines are perpendicular
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Answer 1

To determine whether the lines through the two sets of points intersect, we first need to find the slopes and y-intercepts of both lines.

**First set of points:**
- The coordinates are:
- (-3, 8), (-2, 10), (-1, 12), (0, 14), (1, 16), (2, 18), (3, 20), (4, 22)

To find the slope (m) between any two points, we can use the formula:
\[
m = \frac{(y_2 - y_1)}{(x_2 - x_1)}
\]

Using the points (0, 14) and (1, 16):
\[
m = \frac{(16 - 14)}{(1 - 0)} = \frac{2}{1} = 2
\]

Using the slope-intercept form \(y = mx + b\), we can find the y-intercept (b) by using one of the points. Using (0, 14):
\[
14 = 2(0) + b \Rightarrow b = 14
\]
So the equation for the first line is:
\[
y = 2x + 14
\]

**Second set of points:**
- The coordinates are:
- (-3, -2), (-2, 0), (-1, 2), (0, 4), (1, 6), (2, 8), (3, 10), (4, 12)

Using the same method (using points (0, 4) and (1, 6)):
\[
m = \frac{(6 - 4)}{(1 - 0)} = \frac{2}{1} = 2
\]

Using the point (0, 4) for the intercept:
\[
4 = 2(0) + b \Rightarrow b = 4
\]
So the equation for the second line is:
\[
y = 2x + 4
\]

**Compare the lines:**
1. The equation for the first line is \(y = 2x + 14\).
2. The equation for the second line is \(y = 2x + 4\).

Both lines have the same slope (m = 2), which indicates they are parallel.

**Conclusion:**
The lines are parallel and will never intersect.

So, the answer is:
**No…these lines are parallel.**