Final answer:
To find the value of k that makes the line through (-3,k) and (-1,3k) have a y-intercept of -6, we need to determine the equation of the line and then solve for k. The y-intercept is -6 when k = 2.
Step-by-step explanation:
To find the value of k that makes the line through (-3,k) and (-1,3k) have a y-intercept of -6, we need to determine the equation of the line and then solve for k.
The equation of a line is given by y = mx + b, where m is the slope and b is the y-intercept.
Using the two given points, we can find the slope:
- Calculate the slope: m = (3k - k) / (-1 - (-3)) = k / 2
- Set the y-intercept equal to -6: -6 = m(-3) + b
- Substitute the slope: -6 = (k/2)(-3) + b
- Simplify and solve for b: -6 = (-3k/2) + b, b = -6 + (3k/2)
Therefore, the y-intercept is -6 when k = 2.