We conclude that the slope of the linear equation that passes through the points (9, 1) and (10, -1) is -2.
<h3>
How to get the slope of the line that passes through the points (9, 1) and (10, - 1)?</h3>
A linear equation has the general form:
y = a*x + b
Where a is the slope of the line, and b is the y-intercept.
There is a simple equation to get the slope of a point if we know two points. For a line that passes through ( a, b) and (c, d), the equation for the slope is:
a = (d - b)/(c - a)
In this case we know that our line passes through (9, 1) and (10, -1), then using the above equation, we can see that the slope is:
a = (-1 - 1)/(10 - 9) = -2
We conclude that the slope of the linear equation that passes through the points (9, 1) and (10, -1) is -2.
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Clever !
The two square roots of 50 will do that.
They are irrational numbers, so I can't write down their exact values.
They are approximately +7.0711 and -7.0711 (rounded) .
Answer:
The balloon will not reach 2,500 feet after 4 minutes.
Step-by-step explanation:
The equation of the line in the point-slope form is
A hot air balloon in flight begins to ascend at a steady rate of 120 feet per minute, then the slope is
After 
minutes, the balloon is at an altitude of 
feet. This means, the line passes through the point (1.5, 2,150).
Substitute the slope and point coordinates into the equation:
We know that after 3 minutes, the balloon is at an altitude of 2,330 feet. Check this:
Now, find the height after 4 minutes:
Thus, the balloon will reach only 2,450 feet after 4 minutes.
The line that passes through (0 1) and (1 4) is a linear equation
The equation of the points is y = 3x + 1
<h3>How to determine the equation of the points?</h3>
The points are given as:
(x,y) = (0 1) and (1 4)
Start by calculating the slope (m)
m = (y₂ - y₁)/(x₂ - x₁)
So, we have:
m = (4 - 1)/(1 - 0)
Evaluate
m = 3
The equation is then calculated as:
y = m(x - x₁) + y₁
This gives
y = 3(x - 0) + 1
Evaluate the product
y = 3x + 1
Hence, the equation of the points is y = 3x + 1
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