Question

find an equation of the line satisfying the given conditions. write the equation using function notation. Through (-20,5) and (-36, 9) And can you show me the steps?

Answer 1

Answer:

The equation of the line using function notation is

$y=f(x)=-\frac{1}{4}x$

Step-by-step explanation:

Given points are (-20,5) and (-36, 9)

Now to find the equation of the line passes through these points

Let $(x_{1},y_{1})$ and  $(x_{2},y_{2})$ be the two given points  (-20,5) and (-36, 9) respectively.

To find slope

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{9-5}{-36-(-20)}$

$m=\frac{4}{-36+20}$

$m=\frac{4}{-16}$

$m=-\frac{1}{4}$

Therefore  $m=-\frac{1}{4}$

The equation of the line is of thr form y=mx+c

The point (-20,5) passes through the above line and  $m=-\frac{1}{4}$

$5=-\frac{1}{4}(-20)+c$

$5=5+c$

$c=0$

$y=-\frac{1}{4}x+0$

Therefore  $y=-\frac{1}{4}x$

Therefore the equation of the line using function notation is

$y=f(x)=-\frac{1}{4}x$