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Let's solve the problem in Question 15, which asks us to find the value of \( k \), given that the point \( (14, k) \) lies on the line shown in the graph.

### Step-by-step Solution:

1. **Equation of the line**: 
   - From the graph, we can calculate the slope of the line. By identifying two clear points on the line, say \( (-7, -3) \) and \( (0, 6) \), we can find the slope \( m \) as:
   \[
   m = \frac{6 - (-3)}{0 - (-7)} = \frac{9}{7}
   \]
   
2. **Using the point-slope form**: 
   We can now write the equation of the line using the point-slope form \( y = mx + b \), where \( b \) is the y-intercept. From the graph, we can see that the y-intercept is 6. Thus, the equation of the line becomes:
   \[
   y = \frac{9}{7}x + 6
   \]

3. **Substituting the point (14, k)**:
   To find \( k \), we substitute \( x = 14 \) into the equation of the line:
   \[
   k = \frac{9}{7}(14) + 6
   \]
   Simplifying this:
   \[
   k = \frac{9 \times 14}{7} + 6 = 18 + 6 = 24
   \]

So, \( k = 24 \).

It seems there might be an issue with the answer options, as none of them match the result of \( 24 \). But based on the graph and calculation, this is the correct value of \( k \).

Would you like further details or have any questions about this solution?

Here are 5 related questions to explore further:
1. How do you find the slope of a line using two points?
2. What is the point-slope form of a linear equation?
3. How can you interpret the y-intercept from a graph?
4. What happens if the slope of a line is negative?
5. Can you solve for \( k \) if the line's equation is in standard form?

**Tip**: When reading graphs, always check for clear points to calculate the slope accurately.

A line is shown on the xy-coordinate plane. If (14, k) is a point on this line, find the value of k.

Learn how to find the value of k when given a point (14, k) on a line in the xy-plane. This problem involves concepts of algebra, slopes, and linear equations. Suitable for Grades 8-10.

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