Question

The graph represents y = 1/4x + 1/2

Description


The image shows a graph of a linear equation (a straight line) on a coordinate plane.


Key Features:



Straight Line: The line slopes upwards gently from left to right.

Axes: The x-axis and y-axis are visible, with markings indicating numerical values.

Grid: A grid is present, allowing for easy estimation of coordinates on the line.

Intercepts:

The line appears to cross the y-axis (y-intercept) somewhere around (0, 0.5)

The line appears to cross the x-axis (x-intercept) somewhere around (-3, 0)




Possible Tasks


Based on the image, possible tasks might involve:



Determining the equation of the line (in slope-intercept form, point-slope form, or standard form). This would require estimating the slope and y-intercept.

Finding the x-intercept or y-intercept by reading it directly from the graph or using the equation of the line.

Plotting a point given its coordinates or checking if a certain coordinate lies in the line.

Which ordered pairs represent a point on the line and solutions to the equation? Select all that apply.

Responses
(3, 1)
(3, 1)
(0, 0.5)
(0, 0.5)
(0, -2)
(0, -2)
(-2, 0)
(-2, 0)
(2, 1)
(2, 1)
(6, 2)

Answer 1

To determine which ordered pairs represent points on the line represented by the equation \( y = \frac{1}{4}x + \frac{1}{2} \), we can substitute the x-coordinates of each ordered pair into the equation and see if it yields the corresponding y-coordinates.

1. **(3, 1)**:
- Substitute \( x = 3 \):
\[
y = \frac{1}{4}(3) + \frac{1}{2} = \frac{3}{4} + \frac{2}{4} = \frac{5}{4} \quad (\text{not } 1)
\]
- **Not on the line.**

2. **(0, 0.5)**:
- Substitute \( x = 0 \):
\[
y = \frac{1}{4}(0) + \frac{1}{2} = \frac{1}{2} \quad (\text{is } 0.5)
\]
- **On the line.**

3. **(0, -2)**:
- Substitute \( x = 0 \):
\[
y = \frac{1}{4}(0) + \frac{1}{2} = \frac{1}{2} \quad (\text{not } -2)
\]
- **Not on the line.**

4. **(-2, 0)**:
- Substitute \( x = -2 \):
\[
y = \frac{1}{4}(-2) + \frac{1}{2} = -\frac{1}{2} + \frac{1}{2} = 0 \quad (\text{is } 0)
\]
- **On the line.**

5. **(2, 1)**:
- Substitute \( x = 2 \):
\[
y = \frac{1}{4}(2) + \frac{1}{2} = \frac{1}{2} + \frac{2}{4} = 1 \quad (\text{is } 1)
\]
- **On the line.**

6. **(6, 2)**:
- Substitute \( x = 6 \):
\[
y = \frac{1}{4}(6) + \frac{1}{2} = \frac{6}{4} + \frac{2}{4} = \frac{8}{4} = 2 \quad (\text{is } 2)
\]
- **On the line.**

### Summary:
The ordered pairs that represent points on the line \( y = \frac{1}{4}x + \frac{1}{2} \) are:

- **(0, 0.5)**
- **(-2, 0)**
- **(2, 1)**
- **(6, 2)**