Do the points (-3,-2), (8,42) and (15, 70) lie on the same straight line?

Question

Explain how you found the answer please

Answer 1

Slope Formula

m = y₂- y₁/ x₂ - x₁

Order pairs

(- 3, - 2)(8, 42)

m = 42 - (- 2) / 8 - (- 3)

m = 42 + 2 / 8 + 3

m = 44 / 11

m = 4

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Ordered pairs

(- 3, - 2)(15, 70)

m = 70 - (- 2) / 15 - (- 3)

m = 70 + 2 / 15 + 3

m = 72 / 18

m = 4

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The two slopes are the same and they lie on the same line.

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Answer 2

Here are your three points:
(-3, -2)
(8, 42)
(15, 70)

What you need to do is find the equation of this line and then test all three points with it. Just use the first two points.

(-3, -2)
(8, 42)

Find the slope. The formula is (y2 - y1) / (x2 - x1). Use this formula...

(42 - -2) / (8 - -3)
(42 + 2) / (8 + 3)
44 / 11
4
Your slope is 4. (m = 4) Use this and a point (I'll just use (-3, -2) to get b, the y-intercept.

y = mx + b
y = 4x + b
(-2) = 4 (-3) + b
-2 = -12 + b
b = 10
y = 4x + 10

So your equation is y = 4x + 10. Now all you have to do is test all three points in this equation.

(-3, -2)
y = 4x + 10
(-2) = 4(-3) + 10
-2 = -12 + 10
-2 = -2
Yes, that works.

(8, 42)
y = 4x + 10
(42) = 4(8) + 10
42 = 32 + 10
42 = 42
Yes, that works.

(15, 70)
y = 4x + 10
(70) = 4(15) + 10
70 = 60 + 10
70 = 70
Yes, that works.

Since all of those points work, they are all points lying on that line. So they do all line on the same line! =D

Answer 3

Do the points (-3,-2), (8,42) and (15, 70) lie on the same straight line?
We can draw two lines. One joining (-3, -2) and (8,42)
and the other joining (8,42) and (15, 70) .
It is understood that if both these lines have the same slope they are one line as they pass through a common point (8,42).
Now the slope of the first line is
{42-(-2)}/{8-(-3)}=44/11=4
Slope of second line is
{70-42}/(15-8)=28/7=4
Now we have both lines passing through (8,42) and both have the same slope. That means both lines are the same.
Thus the three points are co linear.

Answer 4

Yes, they are... You just need to check the slopes.
The slope between the first two is...
(42-(-2))/(8-(-3))=4
(70-42)/(15-8)=4
Therefore, you can find an equation that passes through this line... The line is y=4x+c... Solve for c by plugging in any one of the points... 42=4(8)+c => c =14 So the equation of the line that passes through all three points is y=4x+14

Answer 5

Very simple, just take the coordinates and do:

(y1 - y2) / (x1 - x2)

for the first and second points:

(42 - (-2)) / (8 - (-3)) = 44/11 = 4

and again for second and third points:

(70 - 42) / (15 - 8)= 28/7 = 4

If the results are equal, then the points are aligned. So yes, those points lie on the same straight line.

Answer 6

let d points be A(-3,-2) B(8,42) c(15,70)
m1=(42+2)/(8+3)=4
m2=(70-42)/(15-8)= 28/7=4
since slopes are same therefore the points lie on the same straight line

Answer 7

y=mx+b
Assume b=0
y/x=m
In a straight line all points must obey this rule.
42-(-2)/(8-(-3))=m=44/11
(70-42)/(15-8)=28/7=m
44/11=28/7=m
m=4
[70-(-2)]/[15-(-3)]=72/18
=4
All points satisfy the criteria therefore all of your points do lay on the same line.

Answer 8

first difficulty's first, we prefer to get the 'x' fee of Q. undemanding: 2.5+5=7.5 x of Q=7.5 Now, given the slope and a pair of coordinates, you want to cope with to fill into an equation which will produce the fewest variables. therefore it extremely is m=y2-y1/x2-x1 If P is at (2.5, 6) Q is at (7.5, ?) and the slope (m) = 3 Filling into the equation we get: m=y2-y1/x2-x1 3=y2-6/7.5-2.5 3=y2-6/5 Multiply each and every thing by technique of 5 to get rid of the fraction. 5(3)=5(y2-6/5) 15=y2-6 Isolate the variable. -y2=-6-15 get rid of negative variables. -y2/-a million=-6/-a million-15/-a million y2=6+15 y2=21 for this reason, the 'y' fee of Q is 21, making the finest answer be: Q(7.5,21)

Answer 9

yes they do...
first you take any two points and find the equation of the line they fall on..
i chose(-3,-2) and (8,42)
the answer is y=4x+10

then you take another pair of points and find the line they fall on..
i chose(-3,-2) and (15,70)
the answer is y=4x+180

from the two equation, we can see that both of their slopes are alike ( the coefficient of x are the slopes) so they fall on the same line..

Answer 10

Use graph paper and plot the points. Then you can find out for yourself.