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

Question

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 −

y = 1 2 x − 5 2

Answer 1

To find the equation of a line passing through two points, we first need to find the slope of the line.

The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)

Let's use the given points: (-1, 2) and (3, 4)

Using the formula, we get:
m = (4 - 2) / (3 - (-1))
m = 2 / 4
m = 1/2

Now, we can use the slope-intercept form of a line (y = mx + b) to find the equation.

Using the point (-1, 2), we can substitute the values into the equation to solve for b:
2 = (1/2)(-1) + b
2 = -1/2 + b
2 + 1/2 = b
5/2 = b

Now that we have the slope (1/2) and the y-intercept (b=5/2), we can write the equation of the line passing through the two points:
y = (1/2)x + 5/2

So the correct equation is:
C. y = (1/2)x + 5/2