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.

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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.