Question

On a coordinate plane, a line goes through (negative 4, 0) and (0, 2). The graph of the equation y = 1 2 x + 2 is displayed. Which equations would intersect the orange line at the y-intercept? Check all that apply.

Answer 1

To find the y-intercept, you substitute \(x = 0\) into the given equation \(y = \frac{1}{2}x + 2\).

So, when \(x = 0\):

\[y = \frac{1}{2}(0) + 2 = 2\]

Therefore, the point where the orange line intersects the y-axis is \((0, 2)\). The equation for this line is \(y = \frac{1}{2}x + 2\), so it intersects at the point \((0, 2)\). Therefore, any equation that passes through \((0, 2)\) will intersect the orange line at the y-intercept.

Among the provided equations, any equation with a constant term of 2 will satisfy this condition. So, the equations that would intersect the orange line at the y-intercept are:

1. \(y = 2\)

2. \(y = \frac{1}{2}x + 2\)

3. \(y = -3x + 2\)