Here is a function.

coordinate plane with horizontal axis labeled x and vertical axis labeled h of x. a line passes through ordered pairs 0 comma 4, 1 comma 1, 2 comma negative 2, and 3 comma negative 5.

what is the function equation in function notation?

enter your answer in the box. show your work. explain how you found your numbers for the slope and y-intercept.

Step-by-step explanation:

The graph is a straight line graph.

The y axis is h(x) and the x axis is x

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

Looking at the graph

y2 = - 2

y1 = + 4

x2 = 2

x1 = 0

Slope, m = (- 2 - 4)/(2 - 0)

m = - 3

To determine the intercept, c, let us substitute m= - 3, y = - 2 and x = 2 into the slope intercept equation. It becomes

- 2 = - 3×2 + c

- 2 = - 6 + c

c = - 2 + 6 = 4

The equation becomes

h(x) = - 3x + 4

The y intercept is the point at which x = 0. Therefore, the y intercept is

y = -3×0 + 4

y = 4

So the y intercept is 4

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .