high blood pressure and exercise

my mother has high blood pressure, she's overweight. I keep telling her to go jogging with me, but she always brings up her high blood pressure. when she has gone with me, she will not jog, because of her blood pressure. she says she needs to start slow, i agree, but slow does not mean walking  for a week she doesn't really pick up the pace, at all. when she gets winded, she slows down. i think she could start jogging, but then again i'm not a doctor. so my question. does exercise need to be taken that carefully for her, or can i push her to a jog here and there?