Question

Which equation represents the graphed function?

A. y = –2x + 3

B. y = 2x + 3

C. y =1/2x + 3

D. y =1/2 –x + 3

Answer 1

graph pass thru (1,1) and (0,3)

answer is
A. y = –2x + 3

if x = 1 then y = –2x + 3 = -2(1) + 3 = 1
if x = 0 then y = –2x + 3 = -2(0) + 3 = 3

Answer 2

Let

`A(0,3) B(1,1)`

Step 1

Find the slope of the line

we know that

the formula to calculate the slope between two points is equal to

`m=((y2-y1))/((x2-x1))`

substitute the values

`m=((1-3))/((1-0))`

`m=((-2))/((1))`

`m=-2`

Step 2

Find the y-intercept

we know that

the y-intercept is the value of y when the value of x is equal to zero

in this problem the y-intercept is the point
`A(0,3)`

Step 3

Find the equation of the line into slope-intercept form

we know that

the equation of the line into slope-intercept form is equal to

`y=mx+b`

we have

`m=-2`

`b=3` -----> b is equal to the y-coordinate of the y-intercept

substitute

`y=-2x+3`

therefore

the answer is the option A

`y=-2x+3`