Write the equation of a line that has a slope of -2 and goes through the point (0, 3).
1 answer:
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Answer:
The Quebec-City-Windsor Corridor
Explanation:
The population density of Canada is 4 people/km².
The most densely-populated urban areas are Vancouver and Montreal (4800/km²).
The most densely populated region of Canada (80/km²) is the Quebec-City-Windsor Corridor. It contains almost half the population of Canada.
There are two main reasons for this.
(a) Climate
The region is entirely below the 47th parallel, so the summers are warm, the winters are not harsh, and the area is suitable for agriculture.
(b) Location
The corridor is close to the border with the United States and carries the bulk of Canada's trade with them. It makes sense for people to live as close to the US border as possible.
Answer:
y= -7/2x-26/2 or y= -7/2x-13
Explanation:
To solve this question you need all of these formulas:
gradient: , Point-Slope
,
perpendicular m , Midpoint
,
and equation of a line
where m stands for gradient
First things first.
To start you have to know the data of the line that includes the two endpoints, so you calculate its gradient (m) of this line with the gradient fromula: , which equals 4/14 or 2/7
(It can also be called rise/run) (Remember the rule of signs where - and - equal +)
with that information you can proceed with the point-slope or point-gradient formula, so you plug the values: y-(-8) = 2/7 (x-(-9)), which results in y+8=2/7(x+9) and then y+8=2/7x+18/7.
To finish the equation you move eight to the other side. To simplify things you can change it into a fraction as I did, and remember to change signs.
y=2/7x+18/7 -8 -> y=2/7x+18/7-56/7 . This gives us the number of y=2/7x-38/7, which is the equation of the first line.
Now to know the gradient of the second line you apply the formula of perpendicular bisector where m1 x m2 = -1. We know m1 (gradient of the first line) is 2/7, so m2 = = -7/2. m2 is therefore -7/2
Now you have to know the midpoint between the two endpoints, which will act as the start point of the perpendicular bisector
M (midpoint) = , which give us the coordinates of (-2, -6)
(remember, x coordinate is always first)
with this point we can apply again the point-slope formula to know the equation of the line:
y-(-6)=-7/2(x-(-2)) -> y+6=-7/2(x+2) -> y+6=-7/2x - 14/2
Move the 6 to isolate the y
y=-7/2x -14/2 - 12/2
which equals y= -7/2x -26/2
You can check the results in this page: GraphPlotter
https://www.transum.org/Maths/Activity/Graph/Desmos.asp
To make sure the answer is correct.
Hope it helps :)