Diberi persamaan garis lurus AB ialah 3x + ky = 8 dengan k ialah pemalar. Garis lurus AB adalah selari dengan garis lurus yang menyambungkan titik P(-1, 6) dengan titik Q(5, -3). Cari nilai k dan seterusnya hitung pintasan-x bagi garis lurus AB. Given the equation of the straight line AB is 3x + ky = 8 where k is a constant. The straight line AB is parallel to the straight line connecting the point P(-1, 6) with the point Q(5,-3). Find the value of k and then calculate the x-intercept of the straight line AB.

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)

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