Question

A line passes through the points (2, −4) and (6, 10). What is the equation of the line?

A. y = −7/2x + 11/2
B. y = 7/2x + 11
C. y = −7x − 11/2
D. y = 7/2x − 11

Answer 1

The correct answer is option A. y = -7/2x + 11/2.The equation of the line passing through the points (2, -4) and (6, 10) is y = -7/2x + 11/2.

Step-by-step explanation:

To find the equation of the line passing through the points (2, -4) and (6, 10), we need to find the slope and the y-intercept of the line.

Step 1: Find the slope (m) using the formula m = (y2 - y1) / (x2 - x1).
m = (10 - (-4)) / (6 - 2)
m = 14 / 4
m = 7/2

Step 2: Use the slope-intercept form of a linear equation (y = mx + b) to find the y-intercept (b).
Using the point (2, -4):
-4 = (7/2)(2) + b
-4 = 7 + b
b = -4 - 7
b = -11

Therefore, the equation of the line is y = -7/2x - 11/2.