We are given four pairs of points. For each pair there is a line going through both points. We want to know if any of these lines are parallel to a line with a slope of 34. To do so, we will find the slope of the four lines, one at the time, keeping in mind that two lines are parallel if their slopes are equal.
Option F
To find the slope of the line that passes through these two points, we will use the Slope Formula.
We have found that the slope of the line that passes through (0,5) and (- 4,2) is 34. Since it equals the given slope, the two lines are parallel. However, let's check the other choices to double-check.
Option G
To find the slope of the line that passes through these two points, we will use the Slope Formula again.
We arrived at a special case. In mathematics, division by zero is undefined. A line with an undefined slope is a vertical line. Since a line with slope 34 is not a vertical line, the lines are not parallel.
Option J
To find the slope of the line that passes through these two points, we will use the Slope Formula one last time.
We have found that the slope of the line that passes through (0,- 2) and (- 4,- 2) is 0. This is a horizontal line. Since 0 ≠34, the two lines are not parallel.
Conclusion
The only line that is parallel to the one with a slope of 34 is the one that passes through the points (0,5) and (- 4,2). Therefore, the correct option is F.
