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.



To find the equation of the line in slope-intercept form, we use the formula:

\[
y = mx + b
\]

Where:
- \( m \) is the slope of the line
- \( b \) is the y-intercept.

We are given:
- The slope \( m = \frac{1}{2} \)
- The point \( (6, 7) \).

### Step 1: Substitute the point into the slope-intercept equation

The coordinates of the point are \( (x, y) = (6, 7) \), so substitute \( x = 6 \) and \( y = 7 \) into the equation:

\[
7 = \frac{1}{2}(6) + b
\]

### Step 2: Solve for \( b \)

\[
7 = 3 + b
\]

Subtract 3 from both sides:

\[
b = 7 - 3 = 4
\]

### Step 3: Write the equation of the line

Now that we know \( b = 4 \) and \( m = \frac{1}{2} \), we can write the equation of the line:

\[
y = \frac{1}{2}x + 4
\]

This is the equation of the line in slope-intercept form.

Would you like to see more details or ask any questions?

### Related Questions:
1. How do you convert between slope-intercept form and point-slope form?
2. How can you graph a line given its slope and a point?
3. What happens if the slope is negative, and how does it affect the equation?
4. How do you calculate the y-intercept if the equation is given in standard form?
5. What is the significance of the slope in real-world problems?

### Tip:
When writing the equation of a line, it's useful to check your work by substituting the point back into the final equation to verify it holds true.

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.

Learn how to find the equation of a line with a slope of 1/2 passing through the point (6,7) in slope-intercept form. This problem covers key algebraic concepts such as linear equations and slope-intercept form. Suitable for students in Grades 7-9.

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