Question

A line has a slope of 6 and passes through the point (2,7). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

To find the equation of a line in slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), we can use the slope \( m = 6 \) and the point \( (2, 7) \).

1. **Substitute the values into the slope-intercept form:**
We know the slope \( m = 6 \), so our equation starts as:
\[
y = 6x + b
\]

2. **Use the point to solve for \( b \):**
Substitute \( x = 2 \) and \( y = 7 \) into the equation:
\[
7 = 6(2) + b
\]

3. **Calculate \( 6(2) \):**
\[
6(2) = 12
\]
So, we have:
\[
7 = 12 + b
\]

4. **Solve for \( b \):**
\[
b = 7 - 12 = -5
\]

5. **Write the final equation:**
Now that we have \( b = -5 \), the equation of the line is:
\[
y = 6x - 5
\]

Thus, the equation of the line in slope-intercept form is:
\[
\boxed{y = 6x - 5}
\]