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:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{-5+1}{0-5}=\frac{-4}{-5}=\frac{4}{5}$

The equation of the line is:

$y=\frac{4}{5}x+b$

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

$-5=\frac{4}{5}\cdot0+b=b$

Thus, b=-5

The equation of the line is now fully determined:

$y=\frac{4}{5}x-5$

intercept