Line A passes through points (-1, 5) and (3, -1). Line B passes through points (7, 2) and (6, -1). At what point does line A intersect line B?

Question

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Answer 1

The slope of line A is (-1-5)/(3+1)=-6/4=-3/2 and the slope of line B is (-1-2)/(6-7)=-3/-1=3. The intercepts are A for line A and B for line B: y=-3x/2+A, y=3x+B. Substitute (3,-1) to find A: -1=-9/2+A, so A=9/2-1=7/2; and substitute (7,2) to find B: 2=21+B, so B=-19. The two equations are y=-3x/2+7/2 and y=3x-19. When these two are equal we have -3x/2+7/2=3x-19. -3x+7=6x-38 and 9x=45, so x=5. From this we can get y=15-19=-4. The point of intersection is (5,-4).