Question

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.

Answer 1

slope -3 y intercept is 4

Explanation:

slope y2-y1/x2-x1

4-1/0-1 = -3

y=mx+c

y=4-3x

Answer 2

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