Question

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

Answer 1

Equation of a line

The slope-intercept of the equation of a line is given by:

y = mx + b

Where m is the slope and b is the y-intercept

The slope can be calculated with the formula:

`\displaystyle m=(y_2-y_1)/(x_2-x_1)`

Where (x1,y1) (x2,y2) are the points through which the line passes. We are given the points (5,-1) and (0,-5), thus:

`m=(-5+1)/(0-5)=(-4)/(-5)=(4)/(5)`

The equation of the line is:

`y=(4)/(5)x+b`

To determine the value of b, we use any of the given points, for example, (0,-5):

`-5=(4)/(5)\cdot0+b=b`

Thus, b=-5

The equation of the line is now fully determined:

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

intercept