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The equation of a line
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etherealblair
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#1
Find the equation of the line
Last edited by etherealblair; 4 months ago
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booklover1313
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(Original post by etherealblair)
Find the equation of the line
Find the equation of the line
So find the gradient using m = change in y/change in x (pick 2 coordinates and do that)
Then find c, the y-intercept
Or input the values into the equation or y-y1 = m(x-x1), where x1 and y1 are the coordinates of a point on the line
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etherealblair
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#3
[quote=booklover1313;96484397]y=mx + c
So find the gradient using m = change in y/change in x (pick 2 coordinates and do that)
Then find c, the y-intercept
Or input the values into the equation or y-y1 = m(x-x1), where x1 and y1 are the coordinates of a point on the line
I've chosen to coordinates from the graph (0,6) and (3,9) but what do you mean by change in? Do you divide each x coordinate by the y coordinate like ( (0,6÷3,9) or 0÷6 and 3÷9. I've watched a couple videos but they haven't really helped. If you could narrow it down a little more maybe I'll understand better . I don't really understand what I have to do the answer the homework question any more help would be highly appreciated but if you can't it's fine also before I thought the answer was 4x+5=y but my hw site (mathswatch) says it's wrong so idk <33
So find the gradient using m = change in y/change in x (pick 2 coordinates and do that)
Then find c, the y-intercept
Or input the values into the equation or y-y1 = m(x-x1), where x1 and y1 are the coordinates of a point on the line
I've chosen to coordinates from the graph (0,6) and (3,9) but what do you mean by change in? Do you divide each x coordinate by the y coordinate like ( (0,6÷3,9) or 0÷6 and 3÷9. I've watched a couple videos but they haven't really helped. If you could narrow it down a little more maybe I'll understand better . I don't really understand what I have to do the answer the homework question any more help would be highly appreciated but if you can't it's fine also before I thought the answer was 4x+5=y but my hw site (mathswatch) says it's wrong so idk <33
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booklover1313
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#4
(Original post by etherealblair)
(Original post by booklover1313)
y=mx + c
So find the gradient using m = change in y/change in x (pick 2 coordinates and do that)
Then find c, the y-intercept
Or input the values into the equation or y-y1 = m(x-x1), where x1 and y1 are the coordinates of a point on the line
I've chosen to coordinates from the graph (0,6) and (3,9) but what do you mean by change in? Do you divide each x coordinate by the y coordinate like ( (0,6÷3,9) or 0÷6 and 3÷9. I've watched a couple videos but they haven't really helped. If you could narrow it down a little more maybe I'll understand better . I don't really understand what I have to do the answer the homework question any more help would be highly appreciated but if you can't it's fine also before I thought the answer was 4x+5=y but my hw site (mathswatch) says it's wrong so idk <33
y=mx + c
So find the gradient using m = change in y/change in x (pick 2 coordinates and do that)
Then find c, the y-intercept
Or input the values into the equation or y-y1 = m(x-x1), where x1 and y1 are the coordinates of a point on the line
I've chosen to coordinates from the graph (0,6) and (3,9) but what do you mean by change in? Do you divide each x coordinate by the y coordinate like ( (0,6÷3,9) or 0÷6 and 3÷9. I've watched a couple videos but they haven't really helped. If you could narrow it down a little more maybe I'll understand better . I don't really understand what I have to do the answer the homework question any more help would be highly appreciated but if you can't it's fine also before I thought the answer was 4x+5=y but my hw site (mathswatch) says it's wrong so idk <33
If we look at our line, you chose the points (0,6) and (3,9).
Between these points, our x value has increased by 3, from 0 to 3, and our y value has also increased by 3, from 6 to 9.
The equation for finding the gradient is 'change in y' - so this is how much up or down we have gone, divided by the 'change in x' - which is how far along we have gone.
So we would put in gradient (symbol m):
m = (change in y)/(change in x) = (9-6)/(3-0) = 3/3 = 1
So do you see that our change in the y has been positive 3, from 6 to 9. To find that difference, we did the 9-6 on the top of the fraction.
We can now see that our gradient is 1, which means that for every 1 we go along, we will also go 1 up.
To find the y intercept, we can look at the graph. The y intercept is when the line crosses the y axis. We can see that is when the value for x is 0, and the value of y is 6. So the point (0,6).
Therefore our y intercept is going to be 6.
y = mx +c , so we found that m = 1 and c = 6,
so y = 1x + 6 = x + 6
Using the other equation of y-y1 = m(x-x1) - this is good when it is a bit more complicated and we can't see the y intercept clearly
Let's use the point (3,9), so our x1 value is 3 and our y1 value is 9, m is still 1
y-y1 = m(x-x1)
y-9=1(x-3)
y-9=x-3 [add 9 to both sides]
y=x + 6, which is the same as we had before.
Does that make sense? If you have any more questions, just ask
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etherealblair
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#5
(Original post by booklover1313)
So you can look at the gradient as being the rate of the increase or decrease of a line. The line in the question is going up, so we can think 'for every 1 along, how many up do we go?'. That is what the gradient is telling us. So if we had a gradient of 2, we would see that if we went along by 1, so our x value increased by 1, we would go up by 2, so our y value increases by 2.
If we look at our line, you chose the points (0,6) and (3,9).
Between these points, our x value has increased by 3, from 0 to 3, and our y value has also increased by 3, from 6 to 9.
The equation for finding the gradient is 'change in y' - so this is how much up or down we have gone, divided by the 'change in x' - which is how far along we have gone.
So we would put in gradient (symbol m):
m = (change in y)/(change in x) = (9-6)/(3-0) = 3/3 = 1
So do you see that our change in the y has been positive 3, from 6 to 9. To find that difference, we did the 9-6 on the top of the fraction.
We can now see that our gradient is 1, which means that for every 1 we go along, we will also go 1 up.
To find the y intercept, we can look at the graph. The y intercept is when the line crosses the y axis. We can see that is when the value for x is 0, and the value of y is 6. So the point (0,6).
Therefore our y intercept is going to be 6.
y = mx +c , so we found that m = 1 and c = 6,
so y = 1x + 6 = x + 6
Using the other equation of y-y1 = m(x-x1) - this is good when it is a bit more complicated and we can't see the y intercept clearly
Let's use the point (3,9), so our x1 value is 3 and our y1 value is 9, m is still 1
y-y1 = m(x-x1)
y-9=1(x-3)
y-9=x-3 [add 9 to both sides]
y=x + 6, which is the same as we had before.
Does that make sense? If you have any more questions, just ask
So you can look at the gradient as being the rate of the increase or decrease of a line. The line in the question is going up, so we can think 'for every 1 along, how many up do we go?'. That is what the gradient is telling us. So if we had a gradient of 2, we would see that if we went along by 1, so our x value increased by 1, we would go up by 2, so our y value increases by 2.
If we look at our line, you chose the points (0,6) and (3,9).
Between these points, our x value has increased by 3, from 0 to 3, and our y value has also increased by 3, from 6 to 9.
The equation for finding the gradient is 'change in y' - so this is how much up or down we have gone, divided by the 'change in x' - which is how far along we have gone.
So we would put in gradient (symbol m):
m = (change in y)/(change in x) = (9-6)/(3-0) = 3/3 = 1
So do you see that our change in the y has been positive 3, from 6 to 9. To find that difference, we did the 9-6 on the top of the fraction.
We can now see that our gradient is 1, which means that for every 1 we go along, we will also go 1 up.
To find the y intercept, we can look at the graph. The y intercept is when the line crosses the y axis. We can see that is when the value for x is 0, and the value of y is 6. So the point (0,6).
Therefore our y intercept is going to be 6.
y = mx +c , so we found that m = 1 and c = 6,
so y = 1x + 6 = x + 6
Using the other equation of y-y1 = m(x-x1) - this is good when it is a bit more complicated and we can't see the y intercept clearly
Let's use the point (3,9), so our x1 value is 3 and our y1 value is 9, m is still 1
y-y1 = m(x-x1)
y-9=1(x-3)
y-9=x-3 [add 9 to both sides]
y=x + 6, which is the same as we had before.
Does that make sense? If you have any more questions, just ask
Thank you so much for the explanation! I understand this now and I can finally finish the last piece of homework I was struggling on! Thank youuu!!! I hope you have a wonderful day/night! You're the best! <33
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booklover1313
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#6
(Original post by etherealblair)
Thank you so much for the explanation! I understand this now and I can finally finish the last piece of homework I was struggling on! Thank youuu!!! I hope you have a wonderful day/night! You're the best! <33
Thank you so much for the explanation! I understand this now and I can finally finish the last piece of homework I was struggling on! Thank youuu!!! I hope you have a wonderful day/night! You're the best! <33
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