Answer:
b) 2x - y = -4
Step-by-step explanation:
The y-intercept is the y-coordinate of the point (0, b) where the graph crosses the y-axis. It is also the value of y when x = 0.
The crosses the y-axis at point (0, 4). Therefore, the y-intercept, b = 4.
Next, we need to determine which of the given options matches the graph. It helps to transform each of them into their slope-intercept form, y = mx +b:
a) 2x + y = 4
2x - 2x + y = - 2x + 4
y = -2x + 4 (This is not the correct answer because the slope, m = -2. The given graph has a positive slope).
b) 2x - y = - 4
2x - 2x - y = - 2x - 4
-y = -2x - 4
Divide both sides by -1:
[tex]\frac{-y}{-1} = \frac{-2x - 4}{-1}[/tex]
y = 2x + 4 This is the correct answer because it matches the y-intercept (0, 4), and has a positive slope of 2.
We could easily disregard the last two options because both of their y-intercept is 0.
Therefore, the correct answer is Option b) 2x - y = - 4
