28.1k views
0 votes
Let (a,b) be the point of intersection of the line y=2x-10 and the line through (7,8) and (9,0). Compute a+b.

User Lexus
by
8.6k points

1 Answer

4 votes
First, find the eq'n of the line connecting (7,8) and (9,0). The slope of this line is m = rise / run = (0-8) / (9-7), or m = -8/2, or m = -4. Thus, the equation of this line is y-0 = -4(x-9), or y = -4x + 36.

We must now solve simultaneously the system y = -4x + 36, y = 2x - 10. Let's equate these to one another: -4x + 36 = 2x - 10. Thus, 46=6x, or 3x=23, or
x = 23/3. Subbing this value for x into y = 2x - 10 results in y = 2(23/3) - 30/3, or
y = 16/3. Thus, the solution is (23/3, 16/3). a=23/3 and b=16/3.

We are to compute a+b. This is a+b = 23/3 + 16/3, or 39/3, or 13 (answer).
User Rpayanm
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories