Answer:
(8,1)
Step-by-step explanation:
I don't know how you are supposed to answer this, there are several methods. I will use the earliest algebraic method I know, if you were supposed to do this graphically then you should graph these lines on graph paper and see where they cross
line 1: y = (3/4)x - 5
line 2: y = (-1/4)x + 3
at the point these lines cross the x and y values of the two lines are the same, so you can write
y (line 1) = y (line 2) or
(3/4)x - 5 = (-1/4)x + 3, subtract 3 from both sides
(3/4)x - 8 = (-1/4)x, multiply both sides by 4 (to eliminate the denominators)
3x -32 = -x, add x, add 32 to both sides
4x = 32, divide both sides by 4
x = 8, substitute x = 8 into either of the linear equations
y=(3/4)x - 5 = (3/4)(8) - 5 = (24/4) - 5 = 6 - 5 = 1
so the intersection point is (8,1)
Given that the answer worked out well, the graphic method should be good too.
The point that a line with a slope of 3/4 and a y- intercept of -5 intersect a
line with a slope of -1/4 and a y- intercept of 3 is (8, 1)
The first line have a slope of 3/4 and y-intercept of -5. Therefore, the equation can be represented as follows:
y = mx + b
where
m = slope
b = y-intercept
Therefore,
y = 3/4 x - 5
The second line have a slope of - 1/4 and y-intercept of 3. Therefore, the equation can be represented as follows:
y = mx + b
Therefore,
y = - 1/4 x + 3
For the lines to intersect they have to share a common point(x, y).
Therefore, the common point can be found as follows:
y = 3/4 x - 5
y = 3/4(8) - 5 = 1
y = -1/4(8) + 3 = 1
Therefore, the common points where they intersect are (8, 1)
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