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12345 [234]
1 year ago
11

write an equation of the line in point slope form that passes through the given points, (2, 3) and (3,6)

Mathematics
1 answer:
MAVERICK [17]1 year ago
7 0

We need to use the point-to-point equation of the line after finding the point-slope form of the line:

We need to identify the corresponding coordinates:

x1 = 2

y1 = 3

x2 = 3

y2 = 6

Then, we have:

y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)

Thus

y-3=\frac{6-3}{3-2}(x-2)\Rightarrow y-3=\frac{3}{1}(x-2)\Rightarrow y-3=3(x-2)

Then, the line in the point-slope form that passes through the given points (2, 3) and (3,6)​ is

y-3=3(x-2)

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*******ASAP******
alina1380 [7]

Answer:

Part A: We have the points A = ( 1,3 ) , B = ( 3,1 ) and C = ( 3,-3 ).

We will first find the equation of line AB and AC.

Now, the slope of AB is \frac{1-3}{3-1} =\frac{-2}{2} =-1.

So, substituting in y = mx + b along with the point ( 1,3 ) gives,

3 = -1 + b i.e. b = 4.

So, the equation of AB is y = -x + 4.

Further, slope of AC is \frac{-3-3}{3-1} =\frac{-6}{2} =-3.

Again, substituting in y = mx + b along with the point ( 1,3 ) gives,

3 = -3 + b i.e. b = 6

So, the equation of AC is y = -3x + 6.

Using 'zero test', we get that,

y = -x + 4 gives 0 = 4, which is not true.

y = -3x + 6 gives 0 = 6, which is not true.

Hence, the solution region will be away from the origin as shown in the figure 1 below.

Thus, we get the system y>-x+4 and y>-3x+6 containing point B and C.

Part B: We have the equations y = -x + 4 and y = -3x + 6.

Substitute the points B = ( 3,1 ) and C = ( 3,-3 ) into these equations respectively, we get,

y = -x + 4 gives y = -3 + 4 i.e. y = 1

y = -3x + 6 gives y = -3 × 3 + 6 i.e. y = -9 + 6 i.e. y = -3.

Hence, points B and C are the solutions of the system in Part A.

Part C: After plotting y>2x+5, we ca see from the second figure that the points included in the shaded region are D = ( -4,2 ) and E = (-1, 5).

So, Lisa is allowed to attend the schools D and E.

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Answer:

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