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Question 24981: I need help with a problem.We are learning to solve systems by graphing and locating the point of intersection.
I know how to graph each system....by the slope and y-intercept, but when it comes to drawing the graph, the point of intersection is wrong. Is there a special way to start graphing the equation - top to bottom or from bottom to top.
Here are 2 problems: y=3/4x-4 the slope is 3/4
the y-intercept is -4
y=-1/2x+6 slope is -1/2
y-intercept is 6
the point of intersection or coordinates I got was (6,1)
y=-2x+5 slope is -2/1
y-intercept is 5
y=x-10 slope is 1
y-intercept is -10
point of intersection or coordinate i got was (7,-3)
Can there be different coordinates or only one?
Thank you
Found 2 solutions by rapaljer, josmiceli:
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! y=3/4x-4 the slope is 3/4
the y-intercept is -4
y=-1/2x+6 slope is -1/2
y-intercept is 6
the point of intersection or coordinates you got was (6,1). I got (8,2).
y=-2x+5 slope is -2/1
y-intercept is 5
y=x-10 slope is 1
y-intercept is -10
point of intersection or coordinate you got was (7,-3). I got (5,-5).
Are your graphs coming out like this? Your slopes and intercepts look right to me. Are you graphing by hand or by calculator?
R^2 at SCC
Answer by josmiceli(19441)  (Show Source):
You can put this solution on YOUR website! the coordinates at the point of intersection must solve both equations
because the point is ON both equations, so just make sure that is true
(1) y = 3/4x - 4
(2) y = (-1/2)x + 6
subtract (2) from (1)
(3) 0 = (3/4x - 4) - ((-1/2)x + 6)
(4) 0 = (5/4)x - 10
(5) (5/4)x = 10
(6) 5x = 40
(7) x = 8
now solve for y in either equation
(8) y = ((3/4)*8) - 4
(9) y = 6 - 4
(10) y = 2
that means the point (8, 2) is on both lines , thus it is the intersection
check it with the other equation
(11) 2 = ((-1/2) * 8) + 6
is this true?
(12) 2 = -4 + 6
yes
just go through this whith the other equations and you'll get the intersections
remember that TWO lines have to intersect unless they're parallel (same slope)
THREE lines do not necessarily have to intersect all at the same point, though
taken in pairs, they will have intersections, though
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