Suppose that gcd(a,b)=1. Prove that for every integer c, the equation ax+by=c has a solution in integers x and y. [Hint: Find a
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Answer:
see below
Step-by-step explanation:
The point-slope form of the equation of a line is ...
y -k = m(x -h) . . . . . . . . line of slope m through point (h, k)
Comparing this form to the equation you are given, we can match parts to see that ...
- k = -2
- m = -3/4
- h = -4
That is, your line has a slope of -3/4 and goes through the point (-4, -2).
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To graph this line, it is often convenient to start with the given point, then use the slope to find another point. The given point is (-4, -2).
The slope is "rise"/"run". A slope of -3/4 tells you the line will drop 3 units for each 4 units it moves to the right. If we add 4 to the x-value of the given point, we get 0. If we add -3 to the y-value of the given point, we get -5. So, another point on the line is (0, -5).
Knowing these two points, you can draw the line through them to graph the equation.
Answer:
x =
Step-by-step explanation:
Given that y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = - 6 when x = 2, then
- 6 = 2k ( divide both sides by 2 )
- 3 = k
y = - 3x ← equation of variation
When y = - 22, then
- 22 = - 3x ( divide both sides by - 3 )
x = =