Question

Nichior compared the slope of the function graphed to the slope of the linear function that has an x-intercept of 2/3 and a y-intercept of -1. If (x) represents the function with the smaller slope, what is the slope of f(x)? ​

Answer 1

The slope of f(x) is 1.5

Explanation:

step 1

Find the slope of the linear function that has an x-intercept of 2/3 and a y-intercept of -1

so

we have the points

(2/3,0) and (0,-1)

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

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

substitute the values

`m=(-1-0)/(0-2/3)`

`m=(-1)/(-2/3)`

`m=(3)/(2)=1.5`

step 2

Find the slope of the function graphed

take the points

(0,-1) and (3,6) approximately

substitute in the formula

`m=(6+1)/(3-0)`

`m=(7)/(3)=2.33`

step 3

we know that

f(x) represents the function with the smaller slope

The smaller slope is 1.5

therefore

The slope of f(x) is 1.5