Write a linear function, f, with f(5) = -1 and f(0) = -5 f(x)=?

Question

Kinda stuck need help on this problem.

Answer 1

f(5) =-1 is the point (5,-1)

f(0) =-5 is the point (0,-5)

(5,-1) and (0,-5) are two points on a line with slope = (-1--5)/(5-0) = 4/5 = m

that 2nd point is the y intercept= b

y=mx +b is a linear function in slope intercept form

y=4x/5 -5

f(x) = (4/5)x -5

or

5y = 4x-5

Answer 2

Hi Isabel,

If you you have the x,y coordinates for any two points on a line, then you can derive the equation for the line.

1. Here, y=f(x). In other words, y is a function of x. Thus were have the coordinates for the two points 5,-1 and 0,-5 given above.
2. In general the equation for a line is given by the slope, m, of an line is give m = (y1-y2)/(x1-x2). So, since we have two know points, we can find the slope to be m = (-1 -(-5))/(5 - 0) = 4/5.
3. Now that we know the slope, we can set up a slope equation the expresses the slope in terms of ONLY one of the know points an arbitrary (unknown) point x,y. Thus, we know consider only the point 0,5 an get the equation (y - (-5))/(x-0) = 4/5.
4. Now we can solve for y (remember y = f(x)), and will be done. See the completed steps below

=> y + 5 = (4/5)x

=> y = (4/5)x - 5

Thus, f(x) = (4/5)x - 5

Answer 3

x y

5 -1

0 -5

determine slope = (-5--1)/(0-5) = -4/-5 = 4/5

equation of line:

y = mx + b

substitute value of m = slope = 4/5 and one of x, y coordinate (0,-5) to find y-intercept (b)

y = 4/5 (x) + b

-5 = 4/5(0) + b

b = -5

f(x) = 4/5(x) - 5