Answer:
To find the value of k that makes the line \(y = kx + 2\) parallel to the line \(4x - 2y + 25 = 0\), you need to remember that parallel lines have the same slope. The equation \(4x - 2y + 25 = 0\) can be rearranged to slope-intercept form (\(y = mx + b\)), where \(m\) represents the slope:
\[
4x - 2y + 25 = 0 \implies -2y = -4x - 25 \implies y = 2x + 12.5
\]
Now, you can see that the slope of the line \(4x - 2y + 25 = 0\) is \(m = 2\).
To make the line \(y = kx + 2\) parallel to this line, it must also have a slope of \(2\). Therefore, you set \(k\) equal to \(2\):
\(k = 2\)
So, the value of \(k\) that makes \(y = kx + 2\) parallel to \(4x - 2y + 25 = 0\) is \(k = 2\).
Explanation: