The graph represents function 1, and the equation represents function 2: A coordinate plane graph is shown. A horizontal line is graphed passing through the y-axis at y = 3. Function 2 y = 5x + 4 How much more is the rate of change of function 2 than the rate of change of function 1

function 1 : horizontal line....a horizontal line has a rate of change (slope) = 0
function 2: y = 5x + 4.....the rate of change (slope) in y = mx + b form, is in the m position...so the rate of change (slope) is 5.

function 2 is 5 greater then function 1.

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MrRoyal MrRoyal · Answer 2 · 2021-11-11T23:17:31-05:00

The rate of change of a function is its slope

The rate of change of function 2 is 5 greater than the rate of change of function 1

The equation of the graph of function 1 is:

\(\mathbf{y =3}\)

The equation of function 2 is:

\(\mathbf{y =5x +4}\)

A linear equation is represented as:

\(\mathbf{y = mx + b}\)

Where m represents the slope or the rate of change

By comparing \(\mathbf{y = mx + b}\) to \(\mathbf{y =3}\), the rate of change of the equation of function 1 is:

\(\mathbf{m_1 = 0}\)

By comparing \(\mathbf{y = mx + b}\) to \(\mathbf{y =5x +4}\), the rate of change of the equation of function 2 is:

\(\mathbf{m_2 = 5}\)

So, we have:

\(\mathbf{m_1 = 0}\) --- function 1

\(\mathbf{m_2 = 5}\) --- function 2

The difference in their rates is:

\(\mathbf{d = m_2 - m_1}\)

Substitute values for m2 and m1

\(\mathbf{d = 5 - 0}\)

\(\mathbf{d = 5}\)

Hence, the rate of change of function 2 is 5 greater than the rate of change of function 1