Which function translates each point on the graph of y=mx+b so that the slope of the segment from the original point to the translated point is 4/3?

g(x)=m(x+3)+b+4

s(x)=4/3x+b

t(x)=m(x−3)+b+4

h(x)=4/3mx+b

Function transformation involves changing the position of a function

The new function is:[tex]\mathbf{h(x) = \frac 43 mx + b}[/tex]

The function is given as:

[tex]\mathbf{y = mx +b}[/tex]

The ratio of the slopes of both segments is given as:

[tex]\mathbf{Ratio = \frac 43}[/tex]

Let the slope of the new segment be m2.

The slope of [tex]\mathbf{y = mx +b}[/tex] is m.

So, we have:

[tex]\mathbf{m_2 : m = \frac 43}[/tex]

Express as fractions

[tex]\mathbf{\frac{m_2 } m = \frac 43}[/tex]

Multiply both sides by m

[tex]\mathbf{m_2 = \frac 43m}[/tex]

From the list of given options,

[tex]\mathbf{h(x) = \frac 43 mx + b}[/tex] has a slope of [tex]\mathbf{m_2 = \frac 43m}[/tex]

Hence, the required function is:[tex]\mathbf{h(x) = \frac 43 mx + b}[/tex]

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