Sorry! I posted only the beginning of this question before. Here's the whole thing.
Write an equation to express y in terms of x.
X 1 __(blank) 3 4 5
Y 7 12 17 22 __(blank)
y = ________(blank)
I don't understand this one. Can someone please help????
when x goes from 3 to 4, y goes from 17 to 22
This indicates a slope of 5.
This means that we will have something like y=5x
If you look carefully, you can see that all the y values differ by 5, and the x values differ by 1.
So, since y(1)=7, y=5x+2
The rest of the values are easy to fill in now.
I get it now! Thanks so much, Steve!
To write an equation expressing y in terms of x, we need to find a pattern or relationship between the values of x and y. Looking at the given table, we can observe that the values of y are increasing by 5 each time the value of x increases by 1.
To express this relationship algebraically, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
In this case, the slope (m) is equal to 5 because every time x increases by 1, y increases by 5.
Now, let's find the y-intercept (b) by looking at the table. When x = 1, y = 7.
Substituting these values into the equation, we have:
7 = 5(1) + b
Simplifying the equation, we get:
7 = 5 + b
To isolate b, we subtract 5 from both sides:
7 - 5 = b
2 = b
So, the equation that expresses y in terms of x is:
y = 5x + 2
Now we can use this equation to find the missing values in the table.
When x = 2:
y = 5(2) + 2
y = 10 + 2
y = 12
When x = 5:
y = 5(5) + 2
y = 25 + 2
y = 27
Thus, the completed table is:
X 1 2 3 4 5
Y 7 12 17 22 27
And the equation expressing y in terms of x is:
y = 5x + 2