`make` not linking locally installed library automatically (CS50x's cs50.h) - makefile

Question

I am trying to replicate CS50x's sandbox on my Gentoo system, but I am getting this kind of error when running make
% make price
cc price.c -o price
/usr/lib/gcc/x86_64-pc-linux-gnu/9.3.0/../../../../x86_64-pc-linux-gnu/bin/ld: /tmp/cc9TASaL.o: in function `main':
price.c:(.text+0x15): undefined reference to `get_float'
collect2: error: ld returned 1 exit status
make: *** [<builtin>: price] Error 1
For reference, this is the source file:
% cat price.c
#include <stdio.h>
#include <cs50.h>
int main(void)
{
float price = get_float("What's the price?\n");
printf("Your total is %.2f (VAT included)\n", price * 1.22);
}
I have manually installed libcs50 on my system:
# ldconfig -p | grep cs50
libcs50.so.10 (libc6,x86-64) => /usr/local/lib64/libcs50.so.10
libcs50.so (libc6,x86-64) => /usr/local/lib64/libcs50.so
And when I compile the file with
% gcc -lcs50 price.c -o price
I am getting no errors.
Have I configured something wrong on my system, or have I misunderstood how make works?
After watching the lecture, I was under the impression that make would "automagically" add the -lcs50 parameter.
Thanks!
SOLUTION
Set CC, CFLAGS and LDLIBS according to these instructions: https://cs50.readthedocs.io/libraries/cs50/c/ .
All the "automagical" stuff in the lecture videos is possible thanks to those environment variables.

Answer 1

Make has a built-in rule that can build an executable from a single .c file:
%: %.c
# recipe to execute (built-in):
$(LINK.c) $^ $(LOADLIBES) $(LDLIBS) -o $#
That way you don't have to write a Makefile for most simple tasks like this one.
You can find it using make -p | grep -C 3 '%: %.c\b'.
The built-in variable LINK.C evaluates to:
LINK.c = $(CC) $(CFLAGS) $(CPPFLAGS) $(LDFLAGS) $(TARGET_ARCH)
Seeing your last comment, all you have to do it call make while overriding the right variables:
make price CC=clang CFLAGS="-fsanitize=signed-integer-overflow -fsanitize=undefined -ggdb3 -O0 -std=c11 -Wall -Werror -Wextra -Wno-sign-compare -Wno-unused-parameter -Wno-unused-variable -Wshadow" LDLIBS="-lcrypt -lcs50 -lm"