Question

Question 7
(Multiple Choice Worth 2 Points)
(Graphing Linear Equations MC)

Which graph represents the equation y equals one half times x plus 2?
graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1
graph of a line passing through the points negative 2 comma 0 and 0 comma 1
graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2
graph of a line passing through the points negative 4 comma 0 and 0 comma 2

Answer 1

To determine which graph represents the equation \( y = \frac{1}{2}x + 2 \), we can evaluate the y-intercept and the slope of the line.

1. **Y-intercept**: The y-intercept occurs when \( x = 0 \).
- Plugging \( x = 0 \) into the equation:
\[
y = \frac{1}{2}(0) + 2 = 2
\]
This tells us that the line intersects the y-axis at the point (0, 2).

2. **Slope**: The slope of the line is \( \frac{1}{2} \), which means that for every increase of 1 in \( x \), \( y \) increases by \(\frac{1}{2}\).

Now, let's analyze the options given:

1. **Graph of a line passing through the points (-2, -2) and (0, -1)**:
- At \( x = 0 \), \( y \) is -1, which does not match our y-intercept of 2.

2. **Graph of a line passing through the points (-2, 0) and (0, 1)**:
- At \( x = 0 \), \( y = 1\), which does not match our y-intercept of 2.

3. **Graph of a line passing through the points (-2, -3) and (0, -2)**:
- At \( x = 0 \), \( y = -2\), which does not match our y-intercept of 2.

4. **Graph of a line passing through the points (-4, 0) and (0, 2)**:
- At \( x = 0 \), \( y = 2\), which matches our y-intercept.
- The slope can also be checked; from (-4, 0) to (0, 2):
- Change in y = \( 2 - 0 = 2\)
- Change in x = \( 0 - (-4) = 4\)
- Slope = \( \frac{2}{4} = \frac{1}{2} \)

Thus, the correct answer is:

**Graph of a line passing through the points (-4, 0) and (0, 2)**.