Question

Write the equation of the line passing through the points (−1, 2) and (3, 4)
Responses
A. y = 2x − 2
B. y = 2x − 10
C. y = 1/2x + 5/2
D. y = 1/2x - 5/2

Answer 1

are u sure?

Answer 2

To find the equation of a line passing through two points, you can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.

First, find the slope (m) of the line using the formula: m = (y2 - y1) / (x2 - x1)

Using the points (-1, 2) and (3, 4), we have:

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 = mx + b and use one of the given points to solve for b.

Using the point (-1, 2):

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

So the equation of the line passing through the points (-1, 2) and (3, 4) is:

y = 1/2x + 5/2

Therefore, the correct answer is D.

Answer 3

I apologize for the mistake. Let's recalculate the equation:

Using the points (-1, 2) and (3, 4), let's find the slope (m):

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

Now, let's substitute the slope and one of the given points (-1, 2) into the slope-intercept form equation (y = mx + b) to find the y-intercept (b):

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

Therefore, the correct equation of the line passing through the points (-1, 2) and (3, 4) is:

y = 1/2x + 5/2

The correct answer is D.