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vertical translations
For a straight line graph, if the equation of the graph is written is the slope-intercept form, then the line goes up and to the right when the coefficient of x is positive.
The new coordinates are(3 + the old 'x', 2 + the old 'y')
goes through the origin, up and to the right
It is y = x + 4
I am not entirely sure what the equation is supposed to be. However, to translate something 4 units up (4 units in the y-direction), simply replace every "y" in your equation by "y - 4". Simplify the result if you want.
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y = x + 14.
I'm guessing that your equation is y = ax² + c (as there are limitations as to what punctuation, including mathematical symbols, can be put in a question). Increasing c by 4 units shifts the graph 4 units up the y-axis. If you equation was y = ax² - c, then increasing c by 4 units shifts the graph 4 units down the y-axis.
Since the geraph is a picture of the equation, it's almost a father and son relationship. The equation begets the graph. The graph, in turn, admires and looks up to the equation.
Yes, for example if you have y=x but you shifted the equation up 3 units hence: y=x+3. than you will receive a different y from every instance (point) of x. Reference: collegemathhelper.com/2015/11/horizontal-graph-transformations-for.html
I guess you mean 4x + 2y = 12 is changed to 4x + 2y = 36. The graph is translated (shifted) up the 7 axis by 24.
So, if we see the basic equation y=mx+b, we see that m=2, and b=1. If you look closely, this is basic rotation and translation of the original graph. First, I would translate the "mother graph" (y=mx) and then translate one up. Then, we would rotate the graph to the right two units.
vertical translations
You cannot, necessarily. Given a graph of the tan function, you could not.
Normally it would be a point which is 2.5 units to the right of the origin and 3.5 units up.