Question

Find the value of k that makes the line through (-3,k) and (-1,3k) have a y-intercept of -6.

Answer 1

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:

1. Calculate the slope: m = (3k - k) / (-1 - (-3)) = k / 2
2. Set the y-intercept equal to -6: -6 = m(-3) + b
3. Substitute the slope: -6 = (k/2)(-3) + b
4. Simplify and solve for b: -6 = (-3k/2) + b, b = -6 + (3k/2)

Therefore, the y-intercept is -6 when k = 2.