Bot GPT 4-o mini To find the value of \( y \) for the point \( (6, y) \) on a line with a slope of 5 that passes through the point \( (1, 4) \), we can use the formula for the slope between two points, which is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In this case:
- \( (x_1, y_1) = (1, 4) \)
- \( (x_2, y_2) = (6, y) \)
- The slope \( m = 5 \)
Substituting these values into the slope formula, we get:
\[ 5 = \frac{y - 4}{6 - 1} \]
Simplifying the denominator:
\[ 5 = \frac{y - 4}{5} \]
Now, to eliminate the fraction, multiply both sides by 5:
\[ 5 \cdot 5 = y - 4 \]
This simplifies to:
\[ 25 = y - 4 \]
Next, we solve for \( y \) by adding 4 to both sides:
\[ y = 25 + 4 = 29 \]
Therefore, the value of \( y \) is:
\[ \boxed{29} \]
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