Question

The rate of change for the finetion is equal to its Choose two points on the graph to find the rate of change, Let (xr.yi) -(0) Let (x, y)) (2.) (x- . m=y2 YI The equation for the line graphed above shows the equation of the line The y-intercept for the graph is (0.). That is the initial value. So, You already know that m

Answer 1

Given the graph of a line:

The rate of change for the function is equal to its slope m

Choose two points to find the rate of change:

Let ( x1, y1 ) = ( 0, 2 )

Let ( x2, y2 ) = ( 2, 5 )

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{2-0}=\frac{3}{2}$

The y-intercept of the line is the point ( 0, 2 ), that is is the initial value

So, b = 2

you already know that m = 3/2

Substitute those values into the slope-intercept form: y = m * x + b

$y=\frac{3}{2}x+2$

The rate of change for the linear function is 3/2 and its equation is

y = 3/2 x + 2