Answer:
y = -x + 2
Explanation:
Given the two points on the graph, (-2, 4) and (0, 2), we can start by solving for the slope of the line.
Let (x₁, y₁) = (-2, 4)
(x₂, y₂) = (0, 2)
Substitute these values into the following slope formula:
m = (y₂ - y₁)/(x₂ - x₁)
m = (2 - 4) / [0 - (-2)]
m = -2/ (0 + 2)
m = -2/2 = -1
Therefore, the slope of the line is -1.
Next, we need to determine the y-intercept of the line, which is the point on the graph where it crosses the y-axis. Upon observing the graph, it is evident that it crosses the y-axis at point (0, 2), which happens to be one of the points we used to solve for the slope. Its y-coordinate, y = 2, is what we will use as the value of b in the slope-intercept form, y = mx + b.
Therefore, given the slope, m = -1, and the y-intercept, b = 2, the equation of the line is:
y = -x + 2