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To solve the problem of finding the equation of the line that passes through the points \((2, -1)\) and \((4, 7)\) in slope-intercept form, we can follow these steps:

### Step 1: Calculate the Slope (m)
The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Substitute the coordinates \((x_1, y_1) = (2, -1)\) and \((x_2, y_2) = (4, 7)\):

\[
m = \frac{7 - (-1)}{4 - 2} = \frac{7 + 1}{4 - 2} = \frac{8}{2} = 4
\]

So, the slope \(m\) is 4.

### Step 2: Use the Point-Slope Form to Find the Equation
The point-slope form of the equation of a line is:

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

Using the point \((2, -1)\) and the slope \(m = 4\):

\[
y - (-1) = 4(x - 2)
\]

Simplify the equation:

\[
y + 1 = 4(x - 2)
\]

\[
y + 1 = 4x - 8
\]

### Step 3: Solve for y to Get the Equation in Slope-Intercept Form
Now, solve for \(y\):

\[
y = 4x - 8 - 1
\]

\[
y = 4x - 9
\]

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

\[
\boxed{y = 4x - 9}
\]

This is the required equation of the line that passes through the points \((2, -1)\) and \((4, 7)\).

Would you like more details or have any questions about this solution?

### Related Questions:
1. How do you find the equation of a line given the slope and one point?
2. What is the significance of the slope in the equation of a line?
3. How do you convert from point-slope form to slope-intercept

Learn how to find the equation of a line passing through the points (2, -1) and (4, 7) using slope calculation and point-slope form. This problem covers coordinate geometry and linear equations, suitable for Grades 7-9 students.

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