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How do i find through which points the lines pass?

To find the points through which each line \( g_1 \) and \( g_2 \) passes, we can identify two clear points on each line directly from the graph, as this will allow us to write down their equations in the form:

\[
a_1 x + b_1 y = c_1
\]
for \( g_1 \) and
\[
a_2 x + b_2 y = c_2
\]
for \( g_2 \).

### Steps to find the points:

1. **Look at the intersections with the axes**: Each line intersects the \( x \)-axis and \( y \)-axis, and we can use these intersections to determine two points for each line.

2. **Determine Points on \( g_1 \)**:
   - Identify where \( g_1 \) crosses the \( y \)-axis and the \( x \)-axis.
   
3. **Determine Points on \( g_2 \)**:
   - Similarly, identify where \( g_2 \) crosses the \( y \)-axis and \( x \)-axis.

Once these points are identified, we can substitute them into the general line equation forms and solve for the parameters \( a_1, b_1, c_1 \) and \( a_2, b_2, c_2 \).

Would you like me to help identify these points directly from the image? Or, would you like more guidance on setting up and solving the system of equations from these points? 

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Here are some questions that might help further your understanding:

1. What are the coordinates of the intersection points on the \( x \)-axis and \( y \)-axis for each line?
2. How can we use two points on a line to determine its slope and equation?
3. What form of a line equation would you prefer to use in such a case (e.g., point-slope or slope-intercept)?
4. Once you have equations, how do you find the intersection of two lines algebraically?
5. Why is it useful to convert the equations into standard form \( ax + by = c \)?

**Tip:** Intersections with the axes are often the easiest points to determine and use when deriving a line equation.

How do I find through which points the lines g1 and g2 pass?

Learn how to find the points through which the lines g1 and g2 pass, using the coordinate geometry and linear equations method. This problem involves determining intersections with the axes and solving for the parameters a1, b1, c1, a2, b2, and c2. Suitable for Grades 10-12.

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