Answer: The equation is y = -6*x
Step-by-step explanation:
I suppose that we want to find the equation for a line that passes through the point (-1, 6) and the origin (remember that the origin is the point (0,0))
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If this line passes through the points (x₁, y₁) and (x₂, y₂), then the slope of the line is equal to:
a = (y₂ - y₁)/(x₂ - x₁)
Now we know that our line passes through the points (0, 0) and (-1, 6), then the slope is:
a = (6 - 0)/(-1 - 0) = 6/-1 = -6
Then our equation is something like:
y = -6*x + b
To find the value of b we can use the fact that this line passes through the point (0, 0).
This means that when x = 0, y is also equal to zero.
If we replace these values in the equation we get:
0 = -6*0 + b
0 = b
Then our equation is:
y = -6*x
Given:
The pair of points.
5. P(1, 1), Q(–1, –1)
6.
To find:
The distance between the pair of points.
Solution:
Distance formula:
5.
The distance between the pair of points P(1, 1) and Q(–1, –1) is:
Therefore, the distance between P and Q is .
6.
The distance between the pair of point is:
On further simplification, we get
Therefore, the distance between E and F is 6.5 units.
Weight of each rock is 14.8 ounces.
Step-by-step explanation:
Given,
Total number of rocks = 10
6 rocks weigh 10 ounce each
4 rocks weigh 22 ounce each.
To find the the weight of each rock.
Now,
Weight of 6 rocks = 10×6 ounces = 60 ounces
Weight of 4 rocks = 22×4 ounces = 88 ounces
So,
Weight of 10 rocks = 88+60 = 148 ounces
Hence,
Weight of each rock = 148÷10 = 14.8 ounces.