Question

A line has a slope of 5. It passes through the points (1, 4) and (6, y). What is the value of y?

Answer 1

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:

\[
\boxed{29}
\]