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### Problem Statement
We are asked to find the equation of a linear function that passes through the points \((2, 4)\) and \((6, 7)\) and to express the answer in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

### Step 1: Calculate the Slope
The first thing we need to do is find the slope of the line that passes through the given points. The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, \((x_1, y_1) = (2, 4)\) and \((x_2, y_2) = (6, 7)\). Plugging in these values:

\[
m = \frac{7 - 4}{6 - 2} = \frac{3}{4}
\]

So, the slope \(m\) is \(\frac{3}{4}\).

### Step 2: Use the Slope to Write the Equation
Now that we have the slope, we can write the equation of the line. We will use the point-slope form of the equation of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

Let's use the point \((2, 4)\) (you can use either point; the result will be the same). Substituting in the values:

\[
y - 4 = \frac{3}{4}(x - 2)
\]

### Step 3: Simplify to Slope-Intercept Form
Next, we need to rearrange the equation to get it into the slope-intercept form, \(y = mx + b\).

Start by expanding the equation:

\[
y - 4 = \frac{3}{4}x - \frac{3}{4} \times 2
\]

Simplifying further:

\[
y - 4 = \frac{3}{4}x - \frac{6}{4}
\]

To simplify the fraction \(-\frac{6}{4}\):

\[
y - 4 = \frac{3}{4}x - \frac{3}{2}
\]

Now, add 4 to both sides to isolate \(y\):

\[
y = \frac{3}{4}x - \frac{3}{2} + 4
\]

Convert 4 into a fraction with a common denominator:

\[
4 = \frac{8}{2}
\]

So,

\[
y = \frac{3}{4}x + \frac{5}{2}
\]

### Final Answer
The equation of the line in slope-intercept form is:

\[
y = \frac{3}{4}x + \frac{5}{2}
\]

This is the linear equation that passes through the points \((2, 4)\) and \((6, 7)\).

Would you like any further clarification or details on this solution?

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Here are 5 related questions for further practice:
1. How do you determine the y-intercept from the equation of a line?
2. What is the equation of a line that has a slope of \(-\frac{1}{2}\) and passes through the point \((3, 4)\)?
3. Given the equation \(y = -\frac{2}{3}x + 4\), what is the slope and y-intercept of the line?
4. How would you write the equation of a line that is parallel to \(y = \frac{3}{4}x + \frac{5}{2}\) and passes through the origin?
5. What is the equation of a line perpendicular to \(y = \frac{3}{4}x + 2\) that passes through the point \((1, 1)\)?

**Tip:** Always double-check your arithmetic when simplifying fractions and converting between different forms of linear equations.

Learn how to solve a linear equation passing through the points (2, 4) and (6, 7). This problem covers key concepts including slope calculation, point-slope form, and slope-intercept form. Suitable for students in Grades 7-9.

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