Answer:
y = (2/3)x + 1/3
Step-by-step explanation:
Check that a single straight line will actually go through all four of these points. Going from (1, 1) to (4, 3), the 'rise' is 2 and the 'run' is 3, which would make the slope, m, equal rise/run = 2/3. Going from (4,3) to (10, 7), m = rise/run = 4/6 = 2/3 (again).
Let's find the slope-intercept form of the equation of this line: y = mx + b
Arbitrarily choose the point (1, 1). Here x = 1, y = 1 and m = 2/3. Then
we have
1 = (2/3)(1) + b, or 1 = 2/3 + b, so that b must be 1/3.
The equation in question is y = (2/3)x + 1/3
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Answer:
The third side of the triangle is (7a + 2b -1).
Step-by-step explanation:
The length of the first side = (3a +8)
The length of the second side = (5 +b)
Let us assume the third side = m
The perimeter of the triangle = SUM OF ALL 3 SIDES
⇒ (10a + 3b +12) = (3a +8) + (5 +b) + m
or, (10a + 3b +12) = 3a + b + 13 + m
or, m = (10a + 3b +12) -(3a + b + 13)
= 10 a + 3b + 12 - 3a - b - 13
= 7a + 2b -1 = ( 10 - 3a) + (3b -b) + 12 -13
or, m = (7a + 2b -1)
Hence, the third side of the triangle is (7a + 2b -1).
