The graph of f(x) = 0.4x is replaced by the graph of g(x) = 0.4x + k. if g(x) is obtained by shifting f(x) up by 4 units, then what is the value of k? k = 4 k = −4 k equals negative one fourth k equals one fourth

The value of k=4

Step-by-step explanation:

we have

f(x)=0.4x

This function represent a linear direct variation (The line passes through the origin)

we know that

If f(x) is shifting up by 4 units

then

The y-intercept of the function will be the point (0,4)

therefore

The function g(x) will be  > g(x)=0.4x+4 (equation of the line into slope intercept form)

The rule of the translation

f(x) > g(x)

(x,y) > (x,y+4)

The translation is 4 units up

therefore

The value of k=4

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

she will travel a distance in the range of 3 - 11 miles