A student did a 340 page essay for 3/4 hours. how much would it take to do 1 page
1 answer:
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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:
Step-by-step explanation:
We know that one of the endpoints of the line segment is (x+4, 1/2y)
The midpoint of the line segment is (3, -2).
And we want to find the other coordinates in terms of x and y.
To do so, we can use the midpoint formula:
Since we know that the midpoint is (3, -2), let's substitute that for M:
Let's solve for each coordinate individually:
X-Coordinate:
We have:
We know that one of the endpoints is (x+4, 1/2y). So, let's let (x+4, 1/2y) be our (x₁, y₁). Substitute x+4 for x₁. This yields:
Solve for our second x-coordinate x₂. Multiply both sides by 2:
Subtract 4 from both sides:
Subtract x from both sides. Therefore, the x-coordinate of our second point is:
Y-Coordinate:
We have:
Substitute 1/2y for y₁. This yields:
Solve for y₂. Multiply both sides by 2:
Subtract 1/2y from both sides. So:
Therefore, the other coordinate expressed in terms of x and y is: