Which graph represents the linear equation y equals one half times x plus 2 on the coordinate plane?

Question

graph of a line passing through the points 0 comma negative 2 and 2 comma negative 1
graph of a line passing through the points negative 4 comma 0 and 0 comma 2
graph of a line passing through the points negative 5 comma 0 and 0 comma 1
graph of a line passing through the points 0 comma 1 and negative 4 comma 0

Answer 1

To determine which graph represents the linear equation \( y = \frac{1}{2}x + 2 \), we can analyze the intercepts:

1. y-intercept: This occurs when \( x = 0 \): \[ y = \frac{1}{2}(0) + 2 = 2 \] Thus, the y-intercept is \( (0, 2) \).

2. x-intercept: This occurs when \( y = 0 \): \[ 0 = \frac{1}{2}x + 2 \] Rearranging gives: \[ \frac{1}{2}x = -2 \implies x = -4 \] Thus, the x-intercept is \( (-4, 0) \).

Now we compare this with the provided options:

1. Graph with points (0, -2) and (2, -1): The y-intercept is -2, so this is not correct.

2. Graph with points (-4, 0) and (0, 2): This graph has an x-intercept of -4 and a y-intercept of 2, which matches the equation \( y = \frac{1}{2}x + 2 \).

3. Graph with points (-5, 0) and (0, 1): The y-intercept is 1, so this is also not correct.

4. Graph with points (0, 1) and (-4, 0): The y-intercept is 1, so this is not correct.

Therefore, the correct graph is the one that passes through the points (-4, 0) and (0, 2).