Question

Which function represents the graph below?

Answer 1

b

Explanation:

Since it intercepts y at 4, and x at 2, we use y=ax+b and rearrange to get the equation from y=2x+4 to 2x-y=-4

Answer 2

b) 2x - y = -4

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:

`(-y)/(-1) = (-2x - 4)/(-1)`

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