What is the equation of the line that passes through (4, 2) and is parallel to 3x - 2y = -6?
-x+
-x
x-4

The Answer is: The point slope form of the equation that is parallel to the given equation and passes through the point (4, 2) is: y = 3/2x - 4

Step-by-step explanation:

Given point: (4, 2)

Given equation:

3x - 2y = -6

Solve for y, to obtain slope m:

-2y = -6 - 3x

y = 3/2x + 3, so the slope m = 3/2. A parallel line has the same slope.

Use the point slope form and substitute the point (4, 2):

y - y1 = m(x - x1)

y - 2 = 3/2(x - 4)

y - 2 = 3/2x - 6

y = 3/2x - 6 + 2

y = 3/2x - 4

Proof:

Find f(x) for x = 4

f(x) = 3/2(4) - 4

f(x) = 6 - 4 = 2, giving the point (4, 2)

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it