Question

Find an expression for the function f(x) whose graph is a line passing through the points (8,-5) and (-9,2). f(x)=

Answer 1

f(x)=-7/17x-29/17

Explanation:

f(x) =y

(8,-5)..........x1 =8,y1=-5

(-9,2)..........x2=-9,y2 =2

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

m=(2-(-5))/(-9-8)

m=(2+5)/(-17)

m=7/(-17)

m=-7/17

y-y1=m(x-x1)

y-(-5)=-7/17(x - 8)

y+5=-7/17x+56/17

y=-7/17x+56/17-5

y=-7/17x+56/17-85/17

y=-7/17x-29/17

f(x)=-7/17x-29/17

Answer 2

Answer: f(x) = - 7x/17 - 29/17

Explanation:

The expression for the function f(x) would be represented in the slope-intercept form, y = mx + c

Where

c represents the y intercept.

m represents the slope of the line.

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

change in the value of y = y2 - y1

Change in value of x = x2 -x1

The line passes through (8, - 5) and (- 9, 2),

y2 = 2

y1 = - 5

x2 = - 9

x1 = 8

Slope,m = ( 2 - - 5)/(- 9 - 8) = 7/- 17 =

- 7/17

To determine the intercept, we would substitute x = 8, y = - 5 and m = - 7/17 into

y = mx + c. It becomes

- 5 = - 7/17 × 8 + c

- 5 = - 56/17 + c

c = - 5 + 56/17

c = - 29/17

The equation becomes

f(x) = - 7x/17 - 29/17