please help with maths!! equations of linear functions?

Question

a linear function f(x) has ordered pairs (2,4) and (5,10).
a. find its equation
b. determine the value of the function when x =3
c. Find when f(x) = 20

thnks alot please show workin cause im totally lost here!!

Answer 1

A linear function just means that it is a straight line. All lines take the form of the equation "y = m * x + b". 'm' is the slope of the line. To find that, you need two points. It is just Rise over Run or (10-4)/(5-2). After that, you only have to find 'b'. To do that, you just take one point and input the values for m, x, and y. So, it would be 4 = m * 2 + b. Because you just found 'm', you can easily solve for 'b'. That gives you the equation. now, get rid of the 'y', and have x=3. From there you can solve for 'y'. Do the same except have y=20 and then find 'x'. That should solve all 3 parts.

Answer 2

A linear function is a first degree polynomial i.e. the polynomial in which the maximum power of the is independent variable is 1. In geometry it refers to the function which represents a straight line.
Example:
In linear algebra :
f(x) = m*x +c
The equation of a straight line is :
y=f(x) = m*x +c
where, m = slope of the straight line
c = intercept of the line on the y-axis.

In your problem the straight line passes through (2,4) and (5,10)
Hence the equation of the line is satisfied by the co-ordinates of the two points.

4 = m * 2 +c --- Eq -A
10 = m * 5 +c --- Eq-B

From (A)-(B):
-6 = m*(-3)
=> m = 2
Putting the value of m in Eq-A, we get
c = 4 - 2* m = 4 - 2*2 = 0

Answers:
1. Hence the linear function is
f(x) = 2 * x

2. Equation of the line:
y=f(x) = 2*x

3. f(3) = 2*3 = 6

4. f(x) =20 = 2*x
=> x = 10.

Cheers

Answer 3

(a)

Given, f(x) has the following ordered pairs:

(x1, y1) = (2, 4) and

(x2, y2) = (5, 10)



f(x) : y,

Thus, Linear function:

f : y = mx + c,


In this form, the constant m will determine the slope or gradient of the line; and the constant c will determine the point at which the line crosses the y-axis.

m = gradient of the linear equation

= (y2 - y1) / (x2 - x1)

= (10 - 4) / (5 - 2)

= 6/3

= 2

y = 2x + c ................ (1)


Next, find c.

c = point intercept the y-axis,

Thus,

Replace point (x1, y1) = (2, 4) in equation (1):

y = 2x + c

4 = 2(2) + c

4 = 4 + c

c = 0

Thus,

y = 2x + 0

y = 2x

f(x) = 2x


(b)

when x = 3,

f(3) = 2 (3)

f(3) = 6


(c)

when f(x) = 20,

2x = 20

x = 20/2

x = 10

Answer 4

a)
let the equation be y=ax+b
now you have to find a and b
(2,4) is an answer so 4 = 2a+b
(5,10) is an answer so 10=5a+b

10 - 4=5a+b-2a-b
6=3a
a=2

2a+b=4 2(2)+b=4
b=0
so the equation is y=2x

you could directly find this equation by looking at two pairs
as you can see in both pairs the value of y is twice the value of x

b)
x=3 y=2x=2(3)=6

f(x)=y=20 2x=20 x=10
the answer is pair (10,20)

Answer 5

y=ax+b, so for those pairs:

4=2a+b
10=5a+b

b=4-2a, so 10=5a+4-2a

3a=6
a=2 b=0

f(x) y=2x

b. when x=3, y=6

c. 20 = 2x x=10

Answer 6

f(x) - 4 = 2(x - 2)
f(x) = 2x
f(3) = 6
2x = 20
x = 10

Answer 7

d