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:
- The equation for the first line is \(y = 2x + 14\).
- 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.