Question

A line has a slope of
1/2
and passes through the point (6,7). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

To write the equation of a line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can use the given slope and the point through which the line passes.

Given:
- Slope \( m = \frac{1}{2} \)
- Point \( (6, 7) \)

1. Start with the slope-intercept form of the equation:
\[
y = mx + b
\]

2. Substitute the slope \( m \):
\[
y = \frac{1}{2}x + b
\]

3. Use the point \( (6, 7) \) to find \( b \):
Substitute \( x = 6 \) and \( y = 7 \) into the equation:
\[
7 = \frac{1}{2}(6) + b
\]
Calculate \( \frac{1}{2}(6) \):
\[
7 = 3 + b
\]
Now, solve for \( b \):
\[
b = 7 - 3 = 4
\]

4. Now we can write the equation of the line:
\[
y = \frac{1}{2}x + 4
\]

Thus, the equation of the line in slope-intercept form is:
\[
y = \frac{1}{2}x + 4
\]