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 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)
In this case, (x1, y1) = (-1, 2) and (x2, y2) = (3, 4):
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 find the y-intercept (b).
Using the point (-1, 2):
2 = (1/2)(-1) + b
2 = -1/2 + b
2 + 1/2 = b
5/2 = b
Finally, substituting the slope (1/2) and the y-intercept (5/2) into the equation, we have the equation of the line:
y = 1/2x + 5/2
Therefore, the correct answer is C) y = 1/2x + 5/2.
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 = 1/2x + 5/2
D y = 1/2x − 5/2
1 answer