Question

Find an equation of the line passing through the given points. Write the equation in the function notation.

Answer 1

straight line equation

known two points namely (3,4) and (4,1)

the formula looking for equations if known two points is

$\frac{x2 - x1}{x1 - x} = \frac{y2 - y1}{y1 - y}$

You can enter the numbers provided above into the formula

$\frac{x2 - x1}{x1 - x} = \frac{y2 - y1}{y1 - y} \\ \frac{4 - 3}{3 - x} = \frac{1 - 4}{4 - y} \\ \frac{1}{3 - x} = \frac{ - 3}{4 - y} \\ - 9 + 3x = 4 - y \\ y = - 3x + 13$

You can check the function is true or false

(3,4) 3=x and 4=y

y = -3(3) + 13

y = -9 + 13

y = 4 ✔️

*additional :

y = -3x + 19 ===== f(x) = -3x + 19

Answer 2

First you need to find the slope of the line using the given coordinates of the two points.
The slope of the line = (1-4)/(4-3) = -3
Then you choose one pair of the coordinates given, either (3,4) or (4,1) , up to you, to find the equation of the line.
If you choose (3,4)
Then
(y-4)/(x-3) = -3
(y-4) = -3x+9
y = -3x+13

If you choose (4,1),
Then
(y-1)/(x-4) = -3
y-1 = -3x+12
y = -3x+13

So, F(x)=-3x+13