First, I assume that by characteristics of the number_people variable you mean the possible values, such as 1 to 6.
Second, mod$coeff[1] is the intercept of the estimated equation and mod$coeff[2] and mod$coeff[3] are the slope coefficients for the number_people and distance_center variables, respectively. The slope for all of your ablines should be mod$coeff[3], not mod$coeff[2]
Third, the intercepts of the ablines are the intercept of the estimated equation mod$[1] plus the effects of different values of number_people. You need to multiply each possible value of number_people by the slope coefficient for number_people, mod$coeff[2]. Assuming the six possible values are 1 to 6:
abline(mod$coeff[1] + mod$coeff[2]*1, mod$coeff[3], col = 2, lwd = 2)
abline(mod$coeff[1] + mod$coeff[2]*2, mod$coeff[3], col = 2, lwd = 2)
abline(mod$coeff[1] + mod$coeff[2]*3, mod$coeff[3], col = 2, lwd = 2)
abline(mod$coeff[1] + mod$coeff[2]*4, mod$coeff[3], col = 2, lwd = 2)
abline(mod$coeff[1] + mod$coeff[2]*5, mod$coeff[3], col = 2, lwd = 2)
abline(mod$coeff[1] + mod$coeff[2]*6, mod$coeff[3], col = 2, lwd = 2)