(x,8) and (6,-16)
(3,y) and ( 9,15)
(2,y) and (10,15)
The ordered pairs in each exersise are for the same direct viration. find each missing value.
To find the missing values in each exercise, we need to determine the relationship between the two given points and use that relationship to find the missing values.
Exercise 1: (x,8) and (6,-16)
Since the given points are in the form (x, 8) and (6, -16), this suggests that there is a linear relationship between the x-values and the y-values. We can find the equation of the line passing through these two points using the slope-intercept form: y = mx + b.
First, let's calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1).
We have:
m = (-16 - 8) / (6 - x),
m = -24 / (6 - x).
Next, we substitute one of the point coordinates into the equation to find the y-intercept (b). Let's use the point (6, -16):
-16 = m * 6 + b,
-16 = (-24 / (6 - x)) * 6 + b.
To find the value of x, we can solve the equation for b:
-16 = (-24 / (6 - x)) * 6 + b,
-16 = -24 + b,
b = -16 + 24 = 8.
Now we can substitute the value of b back into the equation to find x:
-16 = (-24 / (6 - x)) * 6 + 8,
-16 = (-24 / (6 - x)) * 6 + 8,
-24 = -144 / (6 - x),
-24 = -144 / (6 - x),
-24(6 - x) = -144,
-144 + 24x = -144,
-24x = -288,
x = -288 / -24,
x = 12.
Therefore, the missing value is x = 12.
Exercise 2: (3, y) and (9, 15)
Similarly, let's calculate the slope (m) using the formula:
m = (15 - y) / (9 - 3).
Now, we can substitute one of the point coordinates into the equation to find the y-intercept (b). Let's use the point (9, 15):
15 = m * 9 + b.
To find the value of y, we can solve the equation for b:
15 = m * 9 + b.
Now we can substitute the value of b back into the equation to find y:
15 = m * 9 + b.
Therefore, the missing value is y = .
Exercise 3: (2, y) and (10, 15)
Again, let's calculate the slope (m) using the formula:
m = (15 - y) / (10 - 2).
Now, we can substitute one of the point coordinates into the equation to find the y-intercept (b). Let's use the point (10, 15):
15 = m * 10 + b.
To find the value of y, we can solve the equation for b:
15 = m * 10 + b.
Now we can substitute the value of b back into the equation to find y:
15 = m * 10 + b.
Therefore, the missing value is y = .