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Question
Write the equation of the line that has a slope of 2 and passes through the point (-3,4).
Responses
A y = 2x - 2y = 2x - 2
B y = 2x + 2y = 2x + 2
C y = 2x + 7y = 2x + 7
D y = 2x + 10

Answer 1

[AI-generated answer — Bot GPT 3.5]

The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Given that the slope is 2 and the line passes through the point (-3,4), we can substitute the values into the equation.

y = 2x + b

4 = 2(-3) + b

4 = -6 + b

Adding 6 to both sides, we get

10 = b

Therefore, the equation of the line is y = 2x + 10.

D) y = 2x + 10 is the correct answer.

Answer 2

Write the equation of the line passing through the points (−1, 2) and (3, 4)

Responses
A y = 2x − 2y = 2x − 2
B y = 2x − 10y = 2x − 10
C y =

x +

y = 1 2 x + 5 2
D y =

x −

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the equation of the line passing through the points (-1, 2) and (3, 4), we can use the slope-intercept form of the equation, which is y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope of the line using the two points:

m = (y2 - y1) / (x2 - x1)
m = (4 - 2) / (3 - (-1))
m = 2 / 4
m = 1/2

Now that we have the slope, we can substitute it into the equation:

y = (1/2)x + b

Next, we can solve for the y-intercept b by substituting one of the points into the equation. Let's use the point (-1, 2):

2 = (1/2)(-1) + b
2 = -1/2 + b

To isolate b, let's add 1/2 to both sides:

2 + 1/2 = -1/2 + 1/2 + b
5/2 = b

Now we have the value of b, so we can write the final equation as:

y = (1/2)x + 5/2

The correct answer is C) y = (1/2)x + 5/2.