A line with a slope of 3 passes through the points (2, -1) and (4, 5).
Which of the following is not an
equation of the line that passes
through those points?
B. y = 3x-11
A. y+1 = 3(x-2)
D. y-5 = 3(x-4)
C. y = 3x-7

We conclude that only the equation y = 3x-11 is not an equation of the line that passes through the points.

Hence, option B is correct.

Step-by-step explanation:

Given the points

Finding the slope between (2, -1) and (4, 5)

Using the point-slope form of the line equation

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = 3 and the point (2, -1)

Add 2 to both sides

So, y = 3x+5 is one of the equation lines.

We can also check by substituting the values m = 3 and the point (4, 5)

y - 5 = 3(x-4)

So, y - 5 = 3(x-4) is also one of the equation lines.

Now, let say take the point (4, 5) an substitute in y = 3x-11

y = 3x-11

put x = 4 and y = 5

5 = 3(4)-11

5 = 12-11

5  = 1

FALSE!

Hence, the equation y = 3x-11 does not pass through (4, 5). Thus, the equation y = 3x-11 is not an equation of the line that passes through the points.

Now, let say take the point (4, 5) an substitute in y+1 = 3(x-2)

y+1 = 3(x-2)

put x = 4 and y = 5

5+1 = 3(4-2)

6 = 3(2)

6 = 6

TRUE!

Now, let say take the point (2, -1) an substitute in y+1 = 3(x-2)

-1+1 = 3(2-2)

0 = 0

TRUE!

Thus, the equation y+1 = 3(x-2) is an equation of the line that passes through the points.

Now, let say take the point (2, -1) an substitute in y = 3x-7

y = 3x-7

put x = 2 and y = -1

-1 = 3(2) - 7

-1 = 6-7

-1 = -1

TRUE!

Now, let say take the point (4, 5) an substitute in y = 3x-7

y = 3x-7

put x = 4 and y = 5

5 = 3(4)-7

5 =  12-7

5 = 5

TRUE!

Thus, the equation y = 3x-7 is an equation of the line that passes through the points.

Conclusion:

We conclude that only the equation y = 3x-11 is not an equation of the line that passes through the points.

Hence, option B is correct.

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