Given the equation y=2x-3, if x increases by 1 unit what is the corresponding change in y? And if x decreases by 2 units, what is the corresponding change in y? Would these be written as 2(x+1)-3 and 2(x-2)-3?
Y1 = 2 X1 - 3
Y2 = 2(X1+1) -3
so
Y2 - Y1 = 2 X1 + 2 - 2 X1
= 2
===========================
Y2 = 2 (X1 -2) -3
Y1 = 2 X1 -3
Y2 - Y1 = -4
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that is brute force
but
calculus
dy/dx = 2
so
delta y = 2 delta x
if delta x = +1 then delta y = +2
if delta x = -2 then delta y = -4
When they mean change in y are they talking about the y variable. Would it be the change that would take place if the units are increasing or decreasing by a certain number of units?
*When they mean change in y are they talking about the y variable?
I see your other question. In both questions they are really asking you about slope, constant change in y / change in x
a line of form
y = m x + b
has constant slope between points on the line
m = change in y / change in x
= slope = (Y2-Y1)/ (X2-X1)
To determine the corresponding change in y when x increases by 1 unit, you need to substitute x + 1 into the equation for x and calculate y. Let's start with the given equation:
y = 2x - 3
Now substitute x + 1 for x in the equation:
y = 2(x + 1) - 3
Expanding the expression within the parentheses gives:
y = 2x + 2 - 3
Simplifying further:
y = 2x - 1
Therefore, when x increases by 1 unit, the corresponding change in y is -1. This means y will decrease by 1.
Now let's determine the corresponding change in y when x decreases by 2 units. Similar to the previous case, substitute x - 2 into the equation for x:
y = 2(x - 2) - 3
Expanding the expression within the parentheses gives:
y = 2x - 4 - 3
Simplifying further:
y = 2x - 7
Therefore, when x decreases by 2 units, the corresponding change in y is -7. This means y will decrease by 7.