Answer:
k = 2
x intercept = (-8/3,0)
Step-by-step explanation:
First, we can convert the original equation to slope intercept form, y= mx+b
3x + ky = 8
subtract 3x from both sides to put the y and its coefficient on one side
ky = -3x - 8
divide both sides by k to isolate y
y = (-3/k)x - 8/k
Next, we can find the equation of the line it is parallel to
slope = change in y / change in x = (y₂-y₁)/(x₂-x₁) = (y₁-y₂)/(x₁-x₂) = (-3-6)/(5-(-1)) = -9/6 = -3/2
y = (-3/2)x + b
plug a point (x, y) in to find b
plugging (-1, 6) in
6 = 3/2 + b
subtract 3/2 from both sides to find b
b = 9/2
Line AB:
y = (-3/k)x - 8/k
The line AB is parallel to:
y = (-3/2)x + 9/2
Parallel lines have the same slope. In slope-intercept form, this means that whatever the x is multiplied by is the same. Therefore,
(-3/k) = (-3/2) from the two equations
k = 2
Line AB:
y = (-3/2)x -8/2
= (-3/2)x - 4
The x intercept is when y = 0. Therefore, we have
0 = (-3/2)x - 4
add 4 to both sides to put the x and its coefficient on one side
4 = (-3/2)x
divide both sides by (-3/2) to isolate x
-8/3 = x
x intercept = (-8/3,0)
