(-2, 1/2), (1, -2/3) Find the equation of the line
1 answer:
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Answer:
7x +18y = -5
Step-by-step explanation:
The slope is ...
m = (y2 -y1)/(x2 -x1)
m = (-2/3 -1/2)/(1 -(-2)) = (-7/6)/(3) = -7/18
The y-intercept is ...
b = y -mx
b = 1/2 -(-7/18)(-2) = 1/2 -7/9 = -5/18
Then the slope-intercept form of the equation is ...
y = -7/18x -5/18
Multiplying by 18 and adding the opposite of the x-term gives the equation in standard form. The standard form equation is ...
7x +18y = -5
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2 Answers:
- B) The lines are parallel
- C) The lines have the same slope.
Parallel lines always have equal slope, but different y intercepts.
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Explanation:
Let's solve the second equation for y
3y - x = -7
3y = -7+x
3y = x-7
y = (x-7)/3
y = x/3 - 7/3
y = (1/3)x - 7/3
The equation is in y = mx+b form with m = 1/3 as the slope and b = -7/3 as the y intercept. We see that the first equation, where y was already isolated, also has a slope of m = 1/3. The two equations of this system have the same slope. Choice C is one of the answers.
However, they don't have the same y intercept. The first equation has y intercept b = -4, while the second has b = -7/3. This means that they do not represent the same line. They need to have identical slopes, and identical y intercepts (though the slope can be different from the y intercept of course) in order to have identical lines. So we can rule out choice D and E because of this.
Because the two equations have the same slope, but different y intercepts, this means the lines are parallel. Choice B is the other answer.
Parallel lines never touch or intersect, which in turn means there is no solution point. A solution point is where the lines cross. We can rule out choice A.
I recommend using your graphing calculator, Desmos, GeoGebra, or any graphing tool (on your computer or online) to graph each equation given. You should see two parallel lines forming. I used GeoGebra to make the graph shown below.
Answer: cubic units.
Step-by-step explanation:
You can use this formula for calculate the volume of a cone:
Where "r" is the radius and "h" is the height.
You know that the diameter of the base of the cone measures 8 units, then, the radius can be found by dividing the diameter by 2:
Since you already know that height and the radius, you can substitute them into the formula. Then, the volume of this cone is: