Given y = 5x - 12, how will y change if x a) increases by 5 units and b.) decreases by 4 units?

Question

Homework question, if you couldn't tell. My problem is that I don't know HOW to solve it with so little information, so if you could explain the steps I'd appreciate it!

Answer 1

I'll show you two solutions:

First, you can simply plug in numbers for x and see what y is. For example, take x=1. Then y=5(1)-12= -7. Now increase x by 5 units. Then x would be 1+5=6, and y=5(6)-12=18. So when x increases by 5 units, y increases by 25 units. Likewise, for part b, try x=6 (which gets you y=18) and then drop x by 4 (to x=2), which yields y=5(2)-12= -2. So when x decreases by 4 units y decreases by 20 units.

Here's a better solution, and shows that you really understand this stuff:
We have an equation written in slope-intercept form.
y=5x-12.

From this we know that the slope is 5. Conceptually, what this means is that for every increase in x by 1 unit, y will increase by 5 units. Thus, when x increases 5 units, y increases by 5(5) units=25 units. Likewise, when x drops by 4 units, y drops by 4(5)=20 units.

Answer 2

Take x = 0, then y(0) = 5(0) - 12 = -12
Take x = 5, then y(5) = 5(5) - 12 = 25 - 12 = 13
So when you increase by 5 units, y changes -12-->13 or 25 units

Now if you take x = 4, then y(4) = 5(4) - 12 = 20 - 12 = 8 or y changes -12-->8 = 20 units

Answer 3

Give x some arbitrary number like 6 for instance. now y = 5x6-12. Thats 30 - 12 or 18. Now add 5 units to x. Now x=11. Stick it back in the original formula. Y=5x11 -12 or 55-12 which is 43. 43 -18=25.
Basically when you chang e the value of x, the value of y will change by 5 times as much. The change will be the change in the value of x times the coefficient in front of x.
I'll let you figure out the b questions.

Answer 4

Remember that the slope of the function is 5, meaning for every 1 unit x moves left, y moves 5 units up. So,

a) x increases by 5 units, then y increases by 5*5 = 25 units.

b) x decreases by 4 units, then y decreases by 5*4 = 20 units.

Answer 5

::

y = 5x - 12

If x increases by 5 units then the new y is

y_new = 5(x + 5) - 12 = 5x + 25 - 12 = 5x + 13

If we now subtract the previous equation from the new

y_new - y = 0 + 13 - (-12) = 25

y_new = y + 25

meaning y will increase by 25 units.

Use the same approach for the second part, i.e., plug in (x - 4).

Answer 6

a)
new y=5(x+5)-12
=5x+25-12
=5x-12 + 25
=old y + 25
y increases by 25 units

b)
new y = 5(x-4)-12
=5x-20-12
=5x-12 - 20
=old y-20
y decreases by 20 units

Answer 7

If x goes up by 5, then y goes up by 5*5, or 25.
If x goes down by 4, then y goes down by 5*4, or 20.

If this is not clear, just try some values, eg start with x=10 and then try x=15 (up by 5) and x=6 (down by 4).
.

Answer 8

a)
y=5(x+5)-12
y=5x+25-12
y=5x+13

b)
y=5(x-4)-12
y=5x-20-12
y=5x-32