Question

График функции y=(2a-3)x+a-7 и y=(4a-1)x+5-3a параллельны.Найдите значение параметра a и формулу Каждой функции

Answer 1

y=(2a-3)x+a-7

y=(4a-1)x+5-3a

2a-3=4a-1

2a-4a=-1+3

-2a=2  /:(-2)

a= - 1

y=(2a-3)x+a-7=(2·(-1)-3)x+( - 1)-7=(-2-3)x-1-7= - 5x - 8

y=(4a-1)x+5-3a =(4·(-1)-1)x+5-3·(-1) = ( -4-1)x+5+3 = - 5x+8

Answer 2

If two lines are parallel, they have the same slope. In the given problem, we have two parallel lines represented by the equations:

1. y = (2a - 3)x + a - 7
2. y = (4a - 1)x + 5 - 3a

To find the value of the parameter "a," we need to equate the slopes of these two lines since they are parallel. The slope of a linear function in the form of "y = mx + b" is represented by "m."

Let's find the slopes of both lines:

1. For y = (2a - 3)x + a - 7, the slope (m1) is the coefficient of "x," which is (2a - 3).

2. For y = (4a - 1)x + 5 - 3a, the slope (m2) is the coefficient of "x," which is (4a - 1).

Since the two lines are parallel, we equate their slopes:

(2a - 3) = (4a - 1)

Now, solve for "a":

2a - 3 = 4a - 1 2a - 4a = 3 - 1 -2a = 2 a = 2 / -2 a = -1

Now that we have found the value of "a," let's find the formulas for each function:

1. For y = (2a - 3)x + a - 7, with a = -1:

y = (2(-1) - 3)x + (-1) - 7 y = (-2 - 3)x - 8 y = -5x - 8

2. For y = (4a - 1)x + 5 - 3a, with a = -1:

y = (4(-1) - 1)x + 5 - 3(-1) y = (-4 - 1)x + 5 + 3 y = -5x + 8

So, the value of "a" is -1, and the formulas for the two functions are:

1. y = -5x - 8
2. y = -5x + 8