Question

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

Answer 1

First, we need to find the slope (m) of the line passing through the two given points.
The formula for slope is: m = (y2 - y1) / (x2 - x1)

Let's use the points (-1, 2) and (3, 4) to find the slope:
m = (4 - 2) / (3 - (-1))
m = 2 / 4
m = 1/2

Now that we have the slope, we can use the point-slope form of a line to write the equation.
The point-slope form is: y - y1 = m(x - x1)

Using the point (-1, 2), we can write the equation of the line:
y - 2 = (1/2)(x - (-1))
y - 2 = (1/2)(x + 1)
y - 2 = (1/2)x + 1/2

Now, let's simplify the equation to the slope-intercept form (y = mx + b):
y = (1/2)x + 1/2 + 2
y = (1/2)x + 1/2 + 4/2
y = (1/2)x + 5/2

Therefore, the equation of the line passing through the points (-1, 2) and (3, 4) is y = (1/2)x + 5/2, which is option D.