passes through (2,2) parallel to y=x+4x+2

Let's solve this step-by-step.

### 1. Identify the given line’s slope
The equation you provided is:

\[
y = x + 4x + 2 \quad \text{or} \quad y = 5x + 2
\]

Thus, the slope of this line is **5**.

### 2. Write the equation of the parallel line
Since the new line is **parallel** to the given one, it must have the **same slope**, which is \(m = 5\). Therefore, the general form of the parallel line’s equation is:

\[
y = 5x + b
\]

We need to determine the value of \(b\), the y-intercept, to ensure the line passes through the point \((2, 2)\).

### 3. Substitute the point \((2, 2)\)
We substitute \(x = 2\) and \(y = 2\) into the equation:

\[
2 = 5(2) + b
\]

\[
2 = 10 + b
\]

\[
b = 2 - 10 = -8
\]

### 4. Write the final equation
The equation of the line that passes through \((2, 2)\) and is parallel to \(y = 5x + 2\) is:

\[
y = 5x - 8
\]

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Let me know if any step needs further explanation!

### Related Questions:
1. How do you find the slope of a line from its equation?
2. What does it mean for two lines to be parallel?
3. How do you determine the equation of a line from a point and a slope?
4. How do you write the equation of a line in point-slope form?
5. Can you explain how to convert from point-slope form to slope-intercept form?

**Tip:** Parallel lines always have the same slope, but different y-intercepts unless they are identical lines!

Learn how to find the equation of a line passing through the point (2,2) that is parallel to the line y = 5x + 2. This step-by-step solution covers key algebraic concepts, including calculating the slope of parallel lines and using the slope-intercept form. Suitable for students in Grades 8-10.

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