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
To find the equation of the line passing through two points, we can use the slope-intercept form of a line, which is y = mx + b, where m represents the slope and b represents the y-intercept.
First, let's find the slope of the line using the formula:
m = (y2 - y1)/(x2 - x1)
Using the points (-1, 2) and (3, 4), we can substitute the coordinates into the formula:
m = (4 - 2)/(3 - (-1))
m = 2/4
m = 1/2
Now that we have the slope (m = 1/2), we can substitute it into the slope-intercept form and use one of the given points to solve for the y-intercept (b).
Using the point (-1, 2), we substitute its coordinates into the slope-intercept form:
2 = (1/2)(-1) + b
2 = -1/2 + b
2 + 1/2 = b
4/2 + 1/2 = b
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 option C. y = 1/2x + 5/2.
To find the equation of the line passing through the points (-1, 2) and (3, 4), we can use the slope-intercept form of a linear equation, which is given by y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points into the formula, we have:
m = (4 - 2) / (3 - (-1))
= 2 / 4
= 1/2
Now that we have the slope, we can substitute one of the given points and the slope into the equation y = mx + b to find the y-intercept (b).
Let's use the point (-1, 2):
2 = (1/2)(-1) + b
2 = -1/2 + b
2 + 1/2 = b
4/2 + 1/2 = b
b = 5/2
Therefore, the equation of the line passing through the points (-1, 2) and (3, 4) is:
y = 1/2x + 5/2
So, the correct answer is: C. y = 1/2x + 5/2.
To find the equation of the line passing through the points (-1, 2) and (3, 4), we 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, let's find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1)
Given points: (-1, 2) and (3, 4)
Using the formula: m = (4 - 2) / (3 - (-1))
Simplifying, we get: m = 2 / 4 = 1/2
Now that we have the slope (m), we can use either of the given points and substitute it into the equation y = mx + b to solve for b (the y-intercept).
Using the point (-1, 2):
2 = (1/2)(-1) + b
2 = -1/2 + b
b = 2 + 1/2
b = 5/2
Now that we have the slope (m = 1/2) and the y-intercept (b = 5/2), we can write the equation of the line:
y = 1/2x + 5/2
Therefore, the correct answer is D. y = 1/2x - 5/2.