The linear function f(x) passes through the points (0, 3) and (2, 7) . a few values from the exponential function g(x) are shown in the table. x g(x) −1 23 2 18 3 54 what is the positive difference in the y-intercept value of f(x) and g(x) ? enter your answer in the box.

1 is the positive difference in the y-intercept value of f(x) and g(x)

Step-by-step explanation:

The linear function f(x) passes through the points (0, 3) and (2, 7)

Here (0,3) is the point where f(x) crosses y axis

So y intercept = 3

Now we find g(x)  from the given table

g(x) is an exponential function

General form of exponential function is g(x)= ab^x

Now we use the given values from the table

When x=2  , g(x)= 18

Plug in the values

 => (equation 1)

When x=3  , g(x)= 54

Plug in the values

 => (equation 2)

Divide second equation by first equation

so b = 3

We know 18 = ab^2

Plug in 3 for b

18= 9a

Divide by 9 on both sides

So a= 2

So g(x) becomes

To find y intercept we plug in 0 for x

g(x) = 2(3)^2= 2

So y intercept = 2

y intercept of f(x)  is 3  and y intercept of g(x) is 2

Difference is 3-2 = 1

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form