Answer:
Step-by-step explanation:
To determine the value of k for which the lines y = 3x - 7 and kx + y - 1 = 0 are parallel, we need to compare their slopes.
The slope of a line can be found by looking at the coefficient of x in its equation. In the equation y = 3x - 7, the coefficient of x is 3. Therefore, the slope of the first line is 3.
For the second line, kx + y - 1 = 0, we need to rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope. We can rewrite the equation as y = -kx + 1, so the coefficient of x in this case is -k. Therefore, the slope of the second line is -k.
Since parallel lines have the same slope, we can equate the slopes of the two lines:
3 = -k
To find the value of k, we can solve this equation for k:
-k = 3
Dividing both sides of the equation by -1, we get:
k = -3
Therefore, the value of k that makes the lines y = 3x - 7 and kx + y - 1 = 0
