Answer:
y = -¼x + ½
Step-by-step explanation:
Given points (-2, 1) and (6, -1):
Start by solving for the slope of the line, using the following formula:
m = (y2 - y1)/(x2 - x1)
Let (x1, y1) = (-2, 1)
(x2, y2) = (6, -1)
m = (y2 - y1)/(x2 - x1)
m = (-1 - 1)/[6 - (-2)]
m = -2/(6 + 2) = -2/8 = -¼
Therefore, the slope of the line is m = - ¼.
Next, to determine the y-intercept (b), use one of the given points (6, -1) and the slope, and plug in these values into the slope-intercept form:
y = mx + b
-1 = -¼(6) + b
-1 = -3/2 + b
-1 + 3/2 = -3/2 + 3/2 + b
½ = b
Therefore, the y-intercept, b = ½.
The linear equation of the given graph is:
y = -¼x + ½
