4. 
Which linear function in standard form passes through the points (4, 4) and (6, 5)?
A.2x – 4y = 6
B.2x – y = 4
C.3x – 2y = ‒2
D.x – 2y = ‒4

To find the linear function in standard form that passes through the points (4, 4) and (6, 5), we first determine the equation of the line using these points.

### Step 1: Find the slope of the line
The slope formula for two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Substituting the points \((4, 4)\) and \((6, 5)\):

\[
m = \frac{5 - 4}{6 - 4} = \frac{1}{2}
\]

So, the slope of the line is \( \frac{1}{2} \).

### Step 2: Use the point-slope form of the equation
The point-slope form of a linear equation is:

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

Using the point \((4, 4)\) and the slope \(m = \frac{1}{2}\):

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

### Step 3: Simplify the equation
First, distribute on the right side:

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

Add 4 to both sides to solve for \(y\):

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

### Step 4: Convert to standard form
To write the equation in standard form \(Ax + By = C\), eliminate the fraction by multiplying the entire equation by 2:

\[
2y = x + 4
\]

Now, rearrange it into standard form:

\[
x - 2y = -4
\]

This matches option **D**.

### Final Answer:
The correct answer is **D. \(x - 2y = -4\)**.

Would you like further details or have any other questions?

Here are some related questions for further exploration:
1. How do you find the slope given two points?
2. What is the general process of converting slope-intercept form to standard form?
3. How can you determine if a line is parallel to another using slope?
4. Can you find the equation of a line passing through two points in intercept form?
5. How do we interpret the coefficients of \(x\) and \(y\) in the standard form?

**Tip**: When converting from slope-intercept form to standard form, always clear any fractions first.

Which linear function in standard form passes through the points (4, 4) and (6, 5)? A.2x – 4y = 6 B.2x – y = 4 C.3x – 2y = ‒2 D.x – 2y = ‒4

Learn how to find the linear equation in standard form that passes through the points (4, 4) and (6, 5). This step-by-step guide covers key concepts in algebra, including slope, point-slope form, and converting to standard form. Suitable for students in Grades 8-10.

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