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Hver er jafna línunnar á myndinni hér fyrir neðan?

To identify the equation of the line shown on the graph, let's analyze its slope and y-intercept:

1. **Slope**: The line is rising from left to right, indicating a positive slope. Observing the angle, it appears relatively steep but not as steep as the equation \(y = 3x + 2\).

2. **Y-intercept**: The line crosses the y-axis above zero. By inspecting the position, it appears to cross at approximately \( y = -1.5\), aligning well with the y-intercept of equation **\( G: y = 2x - 1.5 \)**.

3. **Confirmation**:
   - The line has a positive slope, and \(G: y = 2x - 1.5\) is the only equation with a slope of 2 and a y-intercept of -1.5, which matches the graph.

Thus, the equation of the line in the graph is:

\[
\text{G: } y = 2x - 1.5
\]

Would you like further details or have any questions?

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Here are some related questions for further practice:

1. What would the line look like if the slope were negative?
2. How would the line shift if we changed the y-intercept to a positive number?
3. What is the effect of doubling the slope on the graph of a line?
4. How do we determine the equation of a line from two points on the line?
5. How would the equation change if the line were parallel but had a different y-intercept?

**Tip:** For linear equations, the slope-intercept form \( y = mx + b \) quickly shows the slope \( m \) and y-intercept \( b \), making graph analysis straightforward.

Learn how to determine the equation of a line from a graph. This problem covers key algebraic concepts, such as identifying the slope and y-intercept, and using the slope-intercept form y = mx + b. Suitable for students in Grades 8-10.

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