Suppose that y is a linear function of x, and that y = 6 when x = 2 and y = 7 when x = 3. What is y when x = 7?
(2,6) and (3,7)
slope = (7-6)/(3-2) = 1
so if y = m x + b and m = 1 then
y = 1 x + b
now put in a point, any point
like
6 = 1 (2) + b
so
b = 4
and
y = x + 4 (indeed, we could have figured that out with a sketched graph.)
then if = 7 then y = 7 + 4 = 11
Well, I have to say, this linear function sounds like a bit of a straight shooter! If we consider the two given points (2,6) and (3,7), we can find the slope of this humorous linear function. The slope, m, is calculated as the change in y divided by the change in x: m = (7-6)/(3-2) = 1/1 = 1.
Now, armed with this slope, we can write the equation of this straight-laced linear function as y = mx + b, where m is the slope and b is the y-intercept. Since we know the value of y when x = 2, we can plug in these values to find the elusive y-intercept.
6 = 1 * 2 + b
6 = 2 + b
4 = b
So, our equation now becomes y = x + 4. Phew!
Now, for the grand finale! When x = 7, we just need to plug this value into our equation to find the value of y:
y = 7 + 4 = 11.
So, when x = 7, y will be a whopping 11! Hope this little math sideshow brought a smile to your face!
To find the value of y when x = 7, we need to determine the equation that represents the linear relationship between x and y.
We are given that y is a linear function of x, so the equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m), we use the formula:
m = (change in y) / (change in x)
m = (7 - 6) / (3 - 2)
m = 1 / 1
m = 1
Now that we know the slope, we can substitute the values of x and y from one of the given points into the equation to find the value of b.
Using the point (x = 2, y = 6):
6 = 1(2) + b
6 = 2 + b
b = 6 - 2
b = 4
So, the equation that represents the linear relationship between x and y is:
y = x + 4
Now, we can substitute x = 7 into this equation to find the value of y:
y = 7 + 4
y = 11
Therefore, when x = 7, y = 11.
To find the value of y when x = 7, we can start by determining the equation of the linear function using the given information.
Since y is a linear function of x, we can write the equation in the form of y = mx + b, where m represents the slope and b represents the y-intercept.
To find the value of the slope, m, we can use the formula:
m = (change in y) / (change in x)
In this case, when x changes from 2 to 3, y changes from 6 to 7. So, the change in y is 7 - 6 = 1, and the change in x is 3 - 2 = 1.
Therefore, the slope, m, is 1.
Now, we can substitute the value of the slope, m, into the equation with the given point (x, y) = (2, 6) to find the value of b:
6 = 1(2) + b
6 = 2 + b
b = 6 - 2
b = 4
So, the equation of the linear function is y = x + 4.
Finally, we can substitute x = 7 into the equation to find y:
y = 7 + 4
y = 11
Therefore, when x = 7, y = 11.